Vibration suppression of beams traversed by moving loads, using optimal Tuned-Mass-Damper (TMD) systems, is investigated. This study is performed on two different geometrical shapes of the beam, namely, uniform homogenous straight beam, and the uniform homogenous curved beam. Initially, three different models of the moving load on a straight beam were developed using the APDL coding in ANSYS©, a commercially available software. Results obtained from the numerical simulation of either a single moving load or a moving mass on the straight beam were compared and validated with those reported in literature. A comprehensive parameter sensitivity analysis was carried out on the beam traversed by moving load with and without the presence of random base excitation and the effects of different beam parameters on the dynamic response of the system were closely examined. Vehicles travelling on suspension bridges induce undesirable vibration, which must be suppressed to a great extent. A half-car planar model moving on a straight beam is considered to study the suppression of vibration and parameter optimization. Attempt is made to design an optimal TMD system to suppress the induced vibration of the bridge due to the moving vehicle, considerably. Furthermore, the effect of non-symmetrical and side-way motion of vehicles on bridges has been considered when both the torsional and flexural vibrations of the bridge-vehicle have been present. Optimum values of the double-acting TMDs parameters have been found to suppress the combined flexural and torsional vibrations of the supporting beam structure. Similar work has been carried out on a uniform homogenous curved beam traversed by either a moving load or a half-car planner model. The effects of the beam curvature angle and the type of loading are closely studied. Optimum values of the two TMDs were obtained to suppress the combined flexural and torsional vibrations of bridges traversed by traveling vehicles. / UOIT