One of the most characteristic properties of longitudinal waves is the growth of their height near the bank line. This property is especially observed in short longitudinal, the mathematical description of which in terms of mathematical approximation was for the first time given by Stokes. In the present paper, Stokes’ solution generalized to the case of a stationary longitudinal flow is used to estimate the static stability and deformation of the sea shore slope or of the deep see and river channel slopes. The stability of shore slopes of a shallow sea or trapezoidal or triangular channels, which have cross-section dimension commensurable with the longitudinal wave length is estimated on the basis of an approximate solution of three-dimensional wave equations by the Galerkin-Kantorovich method. This solution, while preserving the three-dimensional structure of waves over the bank slope, leads to the results which can be easily used in engineering design.