In this paper, the free and forced vibration of a fixed-free Euler-Bernoulli beam in contact with a rigid cylindrical foundation is studied. One end of the beam is clamped at the top of the rigid cylindrical foundation and the other end is free. The vibrations are separated into upward and downward configurations, since a unilateral constraint is added by the cylindrical foundation. The partial differential equation, describing the transverse vibration of the cantilever beam, and the transversality condition, describing the contact position between the beam and the cylindrical foundation, are derived by calculus of variation and Hamilton's principle. This is a moving boundary problem since the unknown contact position has to be determined as part of the solutions. A Galerkin approximation is used to reduce the partial differential equation to a set of non-linear ordinary differential equations. The transient amplitudes and the phase planes of the vibration and the contact length are simulated by a Runge-Kutta algorithm. The effects of initial condition, radius parameter of the cylindrical foundation, externally static and harmonic excitations are investigated and discussed.