The stress-strain state of the foundations of buildings and structures made of weak viscoelastic soils is considered. The mechanical characteristics of a viscoelastic water-saturated soil base were determined experimentally. A macro sample of soil in a pipe about 1 m high had a water lock on top to create excess pore pressure in the sample. Excessive pore pressure simulated the depth of the sample from the surface. From the experiment, the universal parameter of the kinematic model was determined, and the foundation was calculated. Theoretical data obtained within the framework of a kinematic model considering the viscoelastic properties of the soil are compared with the known Flamant solution and experimental data for a stabilized state of the soil. The deviation of vertical displacements from experimental data is no more than 4 % (one-dimensional case). The deviation of the theoretical solution of the flat Flamant-type problem (considering residual pore pressures) from the known solution of the Flamant problem is 16 %. The proposed calculation method makes it possible to predict the deformation of foundations made of water-saturated viscoelastic soils more accurately than the solution for elastic and elastoplastic soils without the influence of pore pressure. The technique is novel because it allows one to simultaneously consider the soil's residual pore pressures and the soil's viscoelasticity.