Elastic solids and viscose fluids are two categories of engineering materials that their response to applied loads are known very well. There is another category of engineering materials whose response to applied loads is a combination of elastic and viscous materials response; they are viscoelastic materials. The response of viscoelastic materials depends not only on existing stresses but also on the history of applied stresses. Therefore, there is an integral relationship between stresses and strains. The integral form of the stress-strain relation makes the analysis of viscoelastic structures more complicated than elastic structures. The purpose of this thesis is to simplify the complexities of static and buckling analysis of viscoelastic thin plates and to understand the static and buckling behavior of these types of plates better. To solve static problems, first, using Laplace transform, we transform the governing equation to Laplace domain and after simplification, using inverse Laplace transform, again we write the governing equation in time domain and at the end we use Meshless collocation method with radial basis function to solve the equation numerically. To simplify the equation governing buckling of thin viscoelastic plates, we assume that displacement perpendicular to the plate plane is a coefficient of creep compliance. After simplification, we make use of Meshless collocation method with radial basis functions to evaluate critical load of the plate. In all cases, to investigate the capability of Meshless collocation method with radial basis functions, first, we evaluate the response at the beginning of loading, when the effect of viscosity is not activated yet and compare it with the exact solution for corresponding elastic problem. In the following, to show the viscosity effect of viscoelastic material, we evaluate the response at different times and compare them with the results for the finite strip method with step-by-step time discretization. Keywords : Thin Plates, Viscoelastic, Meshless, Buckling, Radial Basis Functions