The central theme of this dissertation is the observation that mechanical waves propagate and scatter at different velocities in biological tissues due to a difference in local material properties (such as viscosity and stiffness), due to the presence of inhomogeneities such as a blood vessel, an axon or a muscle filament. These scattered waves contain information about the characteristic stiffness, viscosity and the mechanical property inhomogeneity of the tissues through which they propagate; this information can aid in non-invasive diagnosis of disease and injury using novel quantitative techniques such as Insonification, Percussion and 1-Norm using Magnetic Resonance Elastography (MRE). The goal of the current work is to lay a foundation for non-invasive, wave-propagation based diagnosis of disease and injury in human organs, by demonstrating the validity and relevance of these aforementioned techniques to be able to detect and quantify the influence of a particular disease/ pathology on biological tissues. Chapter 2 encompasses the development and validation of computational model (in silico) of healthy human lung parenchyma using insonification (generation and transmission of controlled mechanical waves into the human lungs through application of pressure pulse at the trachea) and validating this computational model through performing experiments on healthy human subjects. This experimentally validated comprehensive computational model is then extended to simulate mechanical wave propagation in the airways, parenchyma, and chest wall under normal and pathological conditions that create distributed structural changes (e.g., pneumothoraces) and diffuse material changes (e.g., fibrosis), as well as a localized structural and material changes as may be seen with a neoplasm/ tumor. The computational model predictions of a frequency-dependent decreased sound transmission due to PTX were consistent with experimental measurements reported in previous work. Predictions for the case of fibrosis show that while shear wave motion is altered, changes to compression wave propagation are negligible, and thus insonification, which primarily drives compression waves, is not ideal to detect the presence of fibrosis. Results from the numerical simulation of a tumor show an increase in the wavelength of propagating waves in the immediate vicinity of the tumor region. Chapter 2 then focuses on the extension of a comprehensive computational model of mechanical wave motion in healthy human lung parenchyma, developed and experimentally validated by previous members of our research group using percussion, which involves application of mechanical vibration at the sternum to induce wave motion, and the measurements of surface velocity are performed by a scanning laser Doppler vibrometer (SLDV) or a digital stethoscope on the torso posterior. The current work extends this in-silico model to simulate the pathological condition of pneumonia. It is demonstrated that at higher mechanical frequencies of excitation (300-600 Hz) the path of mechanical wave propagation is primarily through the lobe (region) of the lung affected by pneumonia, which is observed in the form of an increased amplitude of wave motion on posterior surface of torso immediately behind the diseased lung. This finding has inspired the design and development of Tabla, a novel, compact and easy to use device that uses percussion to induce mechanical waves into human lung parenchyma, in order to aid in non-invasive, early-stage diagnosis of pneumonia using a digital stethoscope placed at the torso posterior, enabling a wider access to healthcare for individuals living in remote global locations without the necessity of complex medical examinations such as x-ray computed tomography (CT). Of particular emphasis is the fact that the current work utilizes finite element analysis (FEA) to materialize unique “live visualizations” of propagation of mechanical waves in a cross-sectional slice taken along the chest surface, such a visualization would not have been possible in conventional medical examinations using a stethoscope or CT. The dissertation then dwells on the development, testing and experimental validation of a novel technique, called the 1-Norm, which is a novel waveform analysis technique that can be used to analyze contours of mechanical wave displacement. In this dissertation, the validity and relevance of the 1-Norm technique is demonstrated on data obtained from Magnetic Resonance Elastography (MRE) experiments. The technique of MRE involves 3 steps: excite measure compute. To elaborate, (i) firstly, mechanical wave motion is applied to the biological tissue of interest. This can be done in-vivo using a pillow-like actuator placed in contact with the desired region on the body of the human/ animal subject, or it can be done on excised biological tissues placed inside test tubes, using geometric-focusing technique  to generate concentric wavefronts as in this dissertation; (ii) in the second step, imaging of time-resolved snapshots of mechanical wave motion is performed using MRI (the mechanical motion is encoded into the phase component of the complex-valued wave displacement); (iii) finally, in the third step, inversion of the wave equation is performed to determine the stiffness of the imaged tissue by incorporating the boundary conditions of the applied mechanical vibration. This technique is known as inversion (as derived from “inverse problem”) as this is opposite to the conventional approach (also known as “forward problem” in which the mechanical properties of the tissue/ specimen are already known from rheology, and the wave equation is used to compute the displacement field resulting from an applied mechanical excitation). The inversion process represents an ill-posed problem and poses a challenge for the demarcation of tissue boundaries in heterogeneous tissues. Therefore, the current investigation proposes 1-Norm alternative MRE-based biomarker to stiffness, which relies on ill-posed wave inversion. As a first step, 3D printed fiber phantom with a controlled and pre-determined stiffness and fiber-spacing is used to investigate the effect of fiber spacing on the scattering and elongation of mechanical wavefronts. This is followed by computational analysis (using FEA) to model finite element phantoms containing spherical inclusions (scatterers) instead of crisscrossing fibers, to de-couple the effects of anisotropy from those of inhomogeneity, and to better understand the influence of geometrical shape of the specimen on the values of 1-Norm. It is shown using computational modeling that the effects of anisotropy and shape (geometry), as well as center mismatch fall on the lower harmonics (up to 6). 1-Norm is then defined as the summation of absolute values of harmonics from no. 7 and higher, so as to only include contributions of inhomogeneities. This is followed by a demonstration of the validity and relevance of the 1-Norm technique to be able to quantify changes in the stiffness and mechanical homogeneity due to freezing and thawing of biological tissues. It is observed that freezing and thawing leads to a reduction in the stiffness and in the degree of mechanical property inhomogeneity of biological tissues. The results are validated by comparison to a prior work by other research groups who have reported a reduction in tissue stiffness as a result of freezing and thawing. The next part of the dissertation demonstrates the validity and relevance of the 1-Norm technique to be able to quantify the changes in the brain tissue inhomogeneity of a mouse brain due to the presence of neurodegenerative disease (Alzheimer’s disease). Our results show an increase in the degree of brain mechanical inhomogeneity in 5xFAD species female mouse model, along with a reduction in the overall brain stiffness (which is in line with the findings of research published by other groups). This preliminary investigation on mouse brain proves the capability of 1-Norm to be able to non-invasively quantify the degree of mechanical inhomogeneity of brain due to AD, while at the same time proving to be a prospective alternative to the traditional wave inversion techniques (computation of stiffness) which are ill-posed. It is concluded that further work, including investigation of additional number of mouse brains, as well as histopathology are needed to shed light on the microscale causes of mechanical property inhomogenization in neurodegenerative disease. In conclusion, the current work lays a computational and experimental foundation by extending the applications of two already existing techniques (insonification and percussion) and by developing a novel waveform analysis technique of 1-Norm, which has the potential to be developed as a biomarker for non-invasive detection of disease and injury that lead to heterogeneous changes in tissue mechanical properties such as Alzheimer’s disease and primary sclerosing cholangitis (PSC) of the liver.