In this dissertation, transient analysis of thin and moderately thick isotropic and laminated composite plates is studied through analyzing the problems in frequency domain and using a mesh-free method. To this end, plate theories such as; the kashida; TEXT-ALIGN: justify; LINE-HEIGHT: normal; TEXT-KASHIDA: 0%; TEXT-INDENT: 14.4pt; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr; mso-pagination: widow-orphan; mso-layout-grid-align: none" Since in this study the problems are defined without the effects of viscous damping, the exponential window method (EWM) is used to introduce adequate damping to perform inverse Fourier transformation. In this method an artificial damping is added to the governing equations and after evaluation of the solution, its effect is removed. The solution method used in this research is of a Trefftz type and may be kashida; TEXT-ALIGN: justify; LINE-HEIGHT: normal; TEXT-KASHIDA: 0%; TEXT-INDENT: 14.4pt; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr; mso-pagination: widow-orphan; mso-layout-grid-align: none" To demonstrate the accuracy and the efficiency of the method used in this thesis, the solution of various problems, such as isotropic and laminated composite plates with different shapes and boundary conditions, is presented.The numerical results of these analyses are compared with those of the exact solutions (if available) for each theory used. The results are also compared with those obtained from 3D finite element method, modeled in ANSYS. In wave propogation problems, the group velocity of waves is compared with the exact one obtained from FSDT formulation. It has been concluded that the proposed method is capable of producing results with excellent accuracy in transient analysis of plates through analyzing them in frequency domain. Key words : Isotropic plates, Laminated composite plates, Exponential basis functions, Frequency domain