Seismic waves are of primary concern in research in the field of earth sciences. In this study, we are interested in the elastic wave propagation in frozen soils and rocks. Different theoretical approaches are presented, among which, a formulation based on Biot's theory. The main disadvantage of this model is that more parameters are involved than in the other models and that most of them are semi-empirical. On the other hand, this model describes in a more general and unifying manner the wave propagation in the different types of media encountered. In other respects, one of the interests of this model is its predictive capacity. Indeed, some significant results are predicted such as the presence of attenuation peaks due to the variation in permeability as a function of temperature, as well as the possible propagation of two longitudinal and two transverse waves. The experimental testing has been performed in artificial or real soils. The laboratory results obtained on consolidated samples, such as sintered bronze or overconsolidated clay, or on nonconsolidated samples, such as glass powder or silt, are presented. The experimental results on velocity, attenuation, and dispersion of waves, and on the existence of several longitudinal and transverse waves confirm the theoretical predictions.