This paper presents an electric-analog-computer technique for the analysis of beams on elastic foundations that are subjected to traveling loads. This method is applicable to the study of such conditions as nonuniform beams, load magnitude and velocity variations, and such nonlinear conditions as the beam leaving contact with the foundation for upward deflections. A general set of dimensionless solutions is presented for the specific case of a point load of constant magnitude and velocity traveling over an infinite uniform linear track beam. These show high values of deflection and moment for a rather narrow range of velocity above and below the critical velocities producing peak disturbances. It was found that quite high accelerations are required to produce significantly less disturbance than in the constant velocity case. A range of nonlinear track-bouncing conditions was studied in connection with a specific design problem. For none of these cases could more severe conditions be produced than indicated by the linear solutions.