Abstract: The dynamic problem of elastic foundation beams is usually analyzed by using the analytical and numerical methods, but the numerical method has a large amount of calculation, and the analytical method is usually more efficient. The analytic solution of infinite length Euler-Bernoulli beam on viscoelastic foundation subjected to constant axial pressure and transverse traveling wave is obtained by the Laplace and Fourier transforms. Compared with the numerical simulation results, the correctness of the solution is verified. Taking a long tunnel as an example, the influences of wave frequency, wave velocity and axial force and foundation stiffness on the dynamic response of the long tunnel are analyzed, and its internal force response affected by the wave frequency is obtained. The lower the frequency, the greater the internal force response of the tunnel. The internal force response is affected by the travelling wave velocity. When the travelling wave velocity is close to the critical velocity, the internal force response of the tunnel significantly increases.