Non-destructive testing (NDT) plays an important role in the engineering, construction, and geophysical fields. The application of NDT in civil engineering is broad from quality control, structural health monitoring of infrastructure, geophysical and geotechnical field investigation and material characterization to detection of underground anomaly, among others. One of the frequently used NDT techniques for the characterization of geomaterials is based on the propagation of stress waves generated by an excitation source. However, the existing signal interpretation methods still predominantly rely on empirical relations or subjective judgements that are insufficient for the characterization of multiphase complex geomaterials. This research aims to develop novel physics-based signal interpretation methods to characterize physical and mechanical properties of multiphase geomaterials in both field and laboratory investigation scales. Several hybrid inverse and poromechanical models are developed to characterize dry, saturated, and frozen geomaterials subject to stress waves. First, a highly-efficient semi-analytical elastodynamic forward solver was proposed for the Multichannel Analysis of Surface Waves using the spectral element technique to determine effectively and efficiently the soil stratigraphy as well as soil properties. Next, a coupled piezoelectric and solid mechanics model is proposed to study the real response of the bender element (BE) and its interaction with soil samples in the BE test. A comprehensive laboratory investigation is also performed to better understand the response of the BEs inside different soil types. Then, a two-phase poromechanics-based signal interpretation model is developed for laboratory-scale ultrasonic testing to determine the physical and mechanical properties of saturated soil samples based on the distribution of stress waves. Subsequently, a three-phase poromechanical transfer function model is developed using the spectral element technique for pore-scale characterizations of permafrost samples. Furthermore, a comprehensive ultrasonic testing program is conducted to determine the properties of permafrost samples (e.g., ice content, unfrozen water content, porosity, soil type, and mechanical properties) reconstituted in the laboratory. Thereafter, a hybrid inverse and three-phase poromechanical approach is proposed for in-situ characterization of permafrost sites using surface wave techniques. Finally, the GeoNDT software developed to provide physics-based solutions for the interpretation of NDT measurements used in geotechnical and geophysical applications is presented.