Abstract: Terzaghi’s one-dimensional classic consolidation theory ignores inertia of pore water in saturated soils, and has outstanding differences in its derivation and formulation during various publication periods. This leads to a strange phenomenon that considerable misunderstandings and confusion of it still prevail in the current literature. Within the previous framework of large strain dynamic consolidation theory, a one-dimensional infinitesimal strain consolidation wave model is obtained to consider the effect of inertia of pore water with necessary simplification and hypotheses. The present consolidation wave model is characterized by velocity dispersion and dissipative attenuation. The method of separation of variables is used to obtain an analytical solution for a consolidation wave model under the condition of one-way drainage and instantaneous loading. A numerical case study shows that behaviors of consolidation wave are actually controlled by the value of a dimensionless number $D_{\mathrm{c}}$. For cases of higher values of $D_{\mathrm{c}}$, jump and fluctuation of dimensionless excess pore water pressure between positive and negative values are prone to occur, in contrast with the cases of lower values of $D_{\mathrm{c}}$ that result into special phenomena including the Mandel-Cryer effect observed in laboratory tests. The inherent ambiguities about Terzaghi’s classic theory models proposed in the early stage and the later stage respectively are investigated to draw a conclusion that the early Terzaghi’s (1923,1925) consolidation model can be interpreted as a large strain model with respect to the general soil coordinates contrasted with an infinitesimal strain model with respect to the solid-phase volume coordinates. Accordingly, the present consolidation wave model can be extended to various formulations based on the corresponding coordinate properties. Consolidation wave theory is of significance to probe into an innovative uncertainty principle which shows that for scale model testing, the observed consolidation wave response of undisturbed soil samples cannot equal the response of the same soil in practical conditions. Therefore, it is advisable to pay attention to the size effect of soil samples in consolidation study from the perspective of microscopic soil mechanics. The theoretical precision of evaluated excess pore water pressure by classic Terzaghi’s consolidation model varies with the value of dimensionless quantity $D_{\mathrm{c}}$, which is a vital parameter in the proposed consolidation wave theory.