The internal external resonance response of a beam on a finite length elastic foundation under moving loads is studied. A finite length EulerBernoulli beam model supported on a nonlinear viscoelastic foundation excited by a moving concentrated force is established, and the nonlinear partial differential equation is discretized. When the thirdorder natural frequency and the firstorder natural frequency are three times related, the solvability condition for 3:1 internal resonance is derived by using a multiscale method. The effects of foundation damping and nonlinear stiffness on the free vibration response and forced vibration response of a beam under internal resonance conditions with or without moving loads are studied. On this basis, the stability conditions of the system are determined by using the first Lyapunov method.