The aim of this thesis is to employed Time-Weighted Residual Method to investigate the vibrational behavior of continuous beams under moving loads with arbitrary amplitude and velocity. 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 method used in this thesis is to use pre-integral relationships along with equilibrium equations. In this method, the initial conditions and the equation of equilibrium are precisely satisfied. The kinetic and static conditions of the end member are also established at the end of each time-step in a similar process of finite element method. At first, the Spectral Element Method is described and used for verified the processed method’s results. Then with considering the Bernoulli’s assumptions, the relations related to the solving of single-span beams under the moving- loads were extracted by using the residual-weighted method. Afterward, the relations were improved for continuous beams and beams that connected to a frame. Finally, the Time-Weighted Residual method is used to solve beams under moving mass by considering the inertia of the body passing along the inertia of the beam. The results obtained from solving several examples of multi-span beams indicate the accuracy and speed of the proposed method compared to the Finite Element Method and Spectral Element Method. Key Words Moving Loads, Moving Mass, Time-Weighted Residual Method, Meshless Methods, Continues Beams