Numeric model, methods and algorithm to evaluate the strength of earth dams were developed in the paper using Boltzmann-Volterra hereditary theory of viscoelasticity and Rzhanitsyn relaxation kernel. The estimated results of stress-strain state and strength of earth dams under dynamic effects are considered. The basis of this method is finite-element discretization of structure’s model, which leads to solvable system of integral differential equations and further to step-by-step method of its solution. Reliability of worked out algorithms and programs of design was checked by test examples. Study results of stress-strain state of three (different in height) dams under various effects permit to obtain stresses appearing in them and to reveal the most stressed parts of the structure in both resonant and above resonant modes.