In this paper, we consider the problem of numerical dynamic simulation of bending structural elements made of structurally complex materials (composites, nanomaterials) with the consideration of their internal damping properties. The internal damping is considered nonlocal in time. It depends not only on the strain rate value in current moment, but also on the strain rate values on the whole history of element vibration. The nonlocality level depends on the scale factor that can be determined by the experimental data. The nonlocal in time damping model is integrated into the algorithm of the finite element method – the most widely used numerical method for mechanical systems analysis. The equilibrium equation for a structure in motion is solved numerically using an implicit scheme. In this case, the damping matrix of the calculation model is obtained from the condition of stationarity of the total deformation energy of the moving mechanical system. The previous research shows that the results obtained using such a model approximate the empirically determined dissipative properties of composite elements with sufficient reliability. The article discusses the results of a study of a one-dimensional non-local in time computational model implemented in MATLAB software. The possibility of calibrated model adjustment due to better experimental data approximation is estimated. For this purpose, the modified Newmark method is used. It is shown that it is possible to adjust the attitude and phase of the vibration process using the modified Newmark method.