The article discusses the grounds of buildings and structures from weak viscoelastic soils, the features of the theoretical justification for their deformations. The need for this study is due to the discrepancy between the theory of filtration consolidation and field and laboratory experiments. Within the framework of the proposed model, the constructions of solutions to the problems of loading the ground surface with typical loads that describe the stress-strain state of each phase of a two-phase medium (soil skeleton + pore water) with account of the residual pore pressure. The deviation of the calculated residual pore pressures from the experimental data is not more than 5 % (laboratory experiment), 7 % (full-scale experiment). The calculation method presented in the article allows predicting the deformation of the foundations of structures from weak water-saturated soils.