In this Thesis, the formulation of a step by step solution method for solving the problem of bending and shear wave propagation in Timoshenko beam under various forms of moving loads is developed. Because of two reasons, moving loads analysis will be confronted with complexity: loads on the structure do not have a stable position over time and relationship between load movement and nodal displacement values along the path of loading is complicate. The main idea of ??the proposed method is to use pre-integration relationship along with equilibrium equations. So that the initial conditions can be satisfied accurately and equilibrium equations are obtained using the time weighted residual method. The kinematic and static conditions of the end member are also established at the end of each time step. In this study, at first, by considering Timoshenko beam assumptions, the equations for solving single span beams, by passing various forms of moving loads, are extracted using time weighted residual method. Afterward, the relations were improved for continuous beams and beams that connected to a frame. Finally, using the proposed method, specific forms of moving loads including pedestrian load, random moving load and moving mass are investigated. The results obtained from solving different examples of multi-span beams indicate the high accuracy and speed of the proposed method compared to the finite element method. Key Words Timoshenko Beam, Moving Load, Moving Mass, Pedestrain Excitation, Random Moving Load, Time-Weighted Residual Method, Meshless Methods.