This study analyzes excessive vibrations that occurred on the railway vehicle bogie with the computer simulation of a 4-DOF half car railway bogie dynamic physical model and Euler-Bernoulli flexible bridge beam with the simply supported boundary conditions has been introduced considering some limitations which affect problem formulation. To reduce these excessive vibrations other than conventional suspension systems such as passive one, an active suspension system has been designed and attached to the primary suspension system of the railway bogie car. Then, to control these active suspension systems, a control algorithm based on PID and SMC is considered. The coupled equation of motion of the railway bogie car and flexible Euler-Bernoulli bridge beam is obtained by Hamilton's principle in the time domain with the active suspension system. Finally, to demonstrate the effect of the active suspension system with the PID and SMC algorithm upon these excessive vibrations, a computer simulation has been implemented, and the results are presented comparatively. Consequently, the maximum railway vehicle bogie vertical displacement and vertical acceleration have been significantly reduced.