Plates are one of the most useful parts and pieces of industrial systems and structures which are under load so that most important and extended usage of them is producing structures for example airplane, aircraft, sea structure in mechanical and structural engineering. One of the important points in designing such structure which are under intensive load is forbidding buckle. So for designing in this part, increasing critical buckling load has been offered. in this thesis try to achieve optimum distribution of mass and stiffness for achieving maximum amount for buckling load with use optimization technique in designing optimum thickness of elliptical plate which in that’s buckling analysis, we need to solve an eignvalue problem. Optimization of plate for maximizing buckling load is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are dependent of thickness distribution. Because of complicated geometry and boundary conditions for an elliptical plate, solution of this problem has some difficulty. To achieving optimum thickness topology for elliptical plate, generate mesh and assume that thickness is design variable. So that critical buckling load as a objective function will be maximized. Two types of constrains are in this problem: 1) some of the mass for all elements are constant. 2) thickness of every elements has a constrain on their thickness. Solution of this problem has been solved in two steps. In first step, we solve buckling problem for elliptical plate with constant and variable thickness under different boundary conditions. In this step we use two ways for solve the problem: Reyleigh-Ritz Method and standard finite element. In analysis of second step, results of last step has been optimized and at last with use one of the optimization numerical methods, optimum distribution of mass and stiffness for achieving maximum buckling load under different boundary conditions. In this step, for sensitivity analysis, calculate sense of buckling load according to design variables. So that optimum topology of elliptical plate with different radius ratio under Simple, Clamp, Clamp-Simple, Clamp-Free and Free-Simple boundary conditions. To maximizing buckling load with accurate to constraints and effect of different argument to optimum topology. Keywords Optimization, Buckling, Elliptical Plate, Reyleight-Ritz, Finite Element.