The differential equations of motion governing nonlinear dynamical behavior of elastic Timoshenko beams with damage on viscoelastic foundation are given in this paper. It is known that the derived equations are a set of nonlinear partialdifferential equations. To this end, the Galerkin method is firstly applied to simplify this set of equations, and a set of ordinarydifferential equations are obtained. The Matlab software is then used to simulate the dynamical behaviors of the elastic Timoshenko beams. Meanwhile, the influence of the load and the viscoelastic parameters of foundation and the damage on the dynamic behaviors of beams is also studied. Various numerical methods of nonlinear dynamics are used including time history curves, phasetrajectory diagram, Poincare sections and bifurcation figures. It is found that The stability of movement of the structure is strengthened when the viscoelastic parameters of foundation are increased, but the damage of the Timoshenko beams reduces the stability of movement of the structure.