.... In this thesis, an appropriate method is developed to solve inverse problems defined as identification of dynamic loads on an elastic bar. Inverse problems are those in which some required data such as initial time conditions, boundary conditions, and the solution domain shape are not available at first. The solution of such problems would be determined by employing a set of alternative data inside the domain. In this study, the location and time of dynamic load exerted to a certain bar are estimated by using displacement values which are available for a set of points in the time domain. This is performed by employing least squares method and a step-by-step time-weighted residual method. In this approach, indefinite Load is determined by using the system transformation matrix which is constructed by step-by-step time-weighted residual method. In addition, an adaptive technique is used for improving the accuracy of recovery load and reducing the computational cost. The key point of this solution is utilizing the step-by-step time-weighted residual method in which the main idea is employing pre-integration equations through equilibrium equation. In this method, the equilibrium equation and also the initial conditions and boundary conditions are satisfied by time-weighted residual method at the end of each time step. While no mesh is required for the discretization of the solution domain, one of the important advantages of this method is that it allows for recording the time marching data on the exponential bases’ coefficients; this means that during the solution process these coefficients are modified. In this study, the conventional finite element and Newmark methods are also used to solve different inverse problems and their results are compared with those of the proposed method. To give a good insight to the pros and cons of the method, compared to the finite element method, bars under dynamic loads have been considered as the inverse problems solved. Key words : Inverse Problems, Dynamic Loading Identification, Step-by-Step Time-Weighted Residual Solution, Meshless Method, Exponential Basis Functions, Standard Finite Element Method.