The main objective of this study is to propose an appropriate method for solving inverse problems defined for thin plates with static, time-harmonic and time-dependent loadings. Inverse problems are those for which the data for the solution of differential equations such as the initial time condition, boundary conditions, loading, and the solution domain shape are not clear from the very start. Instead, a set of alternative data is available with which the input parameters are estimated. In this paper, Approximate Green Functions (AGF's) are used to solve the inverse problem. Using such functions, the inverse problems are first converted to a set of direct problems and then each problem is solved, in a meshless style, just by considering a set of domain source points. In order to expand the AGF's for the plates, a numerical local meshless method coupled with the fundamental solution of the plate governing equation is needed. In this method, the domain discretization is performed by a set of nodes while at each node a cloud containing a number of adjacent nodes is defined. The solution to the differential equation within the support of each cloud is written as the summation of two separate parts: i.e. homogeneous and particular parts. The homogeneous part is expressed as a linear combination comprising a set of exponential basic functions (EBFs). The EBFs are determined in such a way that the plate homogeneous differential equation is exactly satisfied. The particular solution is obtained by fundamental solution for the equation governing the plate. In this paper, time harmonic plate problems are analyzed, for the first time, using the local method involving EBFs. Inverse Fourier transformation is then employed to find the solution of the inverse problems in time domain. As the advantages of the method used, reference can be made to the simple employment of EBFs, elimination of the need for meshing, and the capability of solving problems involving internal supports and boundaries. To investigate the accuracy and efficiency of the method proposed in this thesis, a variety of problems for various plates with different geometric shapes and boundary conditions, including the applied problem of explosive load reconstruction, have been presented. In the absence of realistic laboratory data, as the input to the inverse problem, the results of direct solutions using commercial codes, as the SAP software for instance, are used. Key words : Inverse Problems, Loading Identification, Thin Plate, Approximate Green's Functions, Exponential Basic Functions, Meshless Method, Point Support, Force Time History.