In the present analysis, an infinite Euler?Bernoulli beam of constant cross-section resting on an elastic foundation is considered. The beam and foundation are assumed to be homogeneous and isotropic. The foundation is modeled using two parameters with damping. The beam is subjected to a constant point load moving with a constant speed along the beam. An effort has been made to find the solution of the governing differential equation analytically. It gives beam deflection under moving load in closed form for damped case. At subcritical speed the absolute value of the deflection of the beam increases with increase of the load velocity. Peak maximum deflection appears when the load travels at the critical speed.