The analysis of beams on elastic foundation subjected to static and dynamic loads is of great importance in structural engineering and provides useful tools to solve practical problems such as the design of foundations and railways, among others. A particularly important case is the study of the dynamic behavior of these structural elements in the presence of moving loads. This dissertation presents the analysis of prismatic beams of infinite length resting on a Winkler-type elastic foundation, subjected to the action of moving loads and compressive axial forces. Concentrated and uniformly distributed loads of a finite length with constant magnitude or harmonic variation are considered. The beam is described by the linear Euler-Bernoulli theory (classical beam theory), considering the effect of rotational inertia (Rayleigh theory). The nonlinear foundation is described by a cubic constitutive law. For the linear case, an exact analytical solution is obtained using the Fourier transform. The Galerkin method is also employed for analyzing both the linear and nonlinear problems. For this, the free vibration modes of simply-supported or clamped beams, Legendre polynomials and Fourier series are used as interpolating functions. The resulting discretized equations of motion are solved analytically in time domain in the linear case and by numerical integration in the nonlinear case. A parametric analysis for the linear case is conducted, comparing the results obtained by the Galerkin method with the exact solution. For the nonlinear problem, the influence of the nonlinearity of the foundation, the radius of gyration of the beam cross-section, the magnitude of the axial compressive force, the velocity of the moving load and the magnitude and frequency of the moving harmonic loads on the displacements of the beam are studied in detailed.