The man’s ever-increasing need in application of new materials has caused that continuously new materials with optimum properties to be put at the man’s disposal. The composite materials are included among these materials coming into being simultaneously towards using the properties of some substances. The functionally graded materials have gradual change of properties in the length of their thickness using in various industries including airspace. In this project, the buckling load analysis of rectangular plate from the functionally graded material quality the thickness of which changes in sinusoidal form on the length and width of the plate. The plate thickness is fixed at the beginning and ending, and gradually moving towards the plate center decreasing from the plate thickness. The Poisson's ratio because of little changes is taken as fixed. The Module Elasticity constantly changes in the length of plate. The compound substance is made from metal and ceramic, the metal quality of which is aluminum. The materials of FGM are compound in the form of heterogeneous microscope and the mechanic properties of them change constantly from one level to another. These materials are a connection made of metal and ceramic or different metals. Ceramic materials are useful in high temperature pressure tensions. The materials properties are unique because of composition nature and soft changes of physical properties in joint section of the material. They are accompany the decrease in residue tensions and decrease of tensions concentration in joint sections and increase of mechanic properties. The most important different between FGM material and conventional heterogeneous materials in requirements of materials targeted, plan and control of microstructure heterogeneous material. Therefore, the way of FGM materials are usable in different fields; for example, where different materials has been placed in one material. It is considerable which all were heterogeneous composition and there was a balance among their parts that this balance must be between virtues of parts properties of composite. But in FGM materials, the balance was destroyed, in general, each element could independently protect its property. In FGM materials, the property changes from one side to another side. For instance, one side has a good mechanic resistance and another one has a high heat resistance, it means that a material has two applied aspects, this is another advantage of FGM material. Another advantage of FGM material is being ceramic-metal in which the part of ceramic provides an extremely high resistance while the part of metal prevents it from breaking. In this project, the influence of plate parameters on buckling instability of FGPs is investigated. The plate is graded through the thickness direction according to a power law function. The boundary conditions along the four edges of the plate are assumed to be fixed-simply supported and clamped. In order to obtain the buckling load of plate, has been utilized the Galerkin’s method. The buckling load in the form of a fixed force in axial basis is affected in the direction of X. The plate stress and strai equations have been calculated by classical plate theory. Keywords: Functionally Graded Material, Bucking, Galerkin’s Method, Variable Thickness.