In present paper the problem about the forced vibrations of hydraulic engineering constructions such as dams is considered in view of hydrodynamical pressure of water and seismic loading. The equations of movement concerning function of deflections are described by the integral-differential equations (IDE) in partial derivatives. 

As a kernel of relaxation it is used weakly singular kernel of Koltunov-Rzanitsyn type. By means of Bubnov-Galerkin method based on polynomial approximation of deflections, the problem is reduced to the solution of nonlinear ordinary IDE, where an independent variable is time. 

Decisions of IDE are determined by the numerical method based on exception of feature in a kernel. On the basis of this method the algorithm of the numerical decision is described. 

The analysis of influence of viscoelastic and nonlinear properties of a material, and also hydrodynamical pressure of water on deflected mode a dam-plate is carried out.