Most researches being done in the field of local buckling of plates with elastic restraints have been confined to plates tied to the foundations. However in many structures, the foundation has a tensionless behavior, for example, a plate resting on a rigid surface in which only the outward movement of the plate relative to the foundation is allowed. The type of restraint in which the structure is restricted to move or buckle in one direction is defined as the unilateral boundary condition. Unilateral buckling is known as a contact problem in the mathematical literature. Research into unilaterally restrained structures mainly requires numerical techniques to solve, and so studies of their behavior have been limited to the last 30 years or so. Penalty method, mathematical programming and direct substitution of buckling mode shapes are three prevalent methods in the literature for investigating the behavior of these structures. In present research the unilateral buckling behavior of point restrained rectangular Functionally Graded Material plates is studied. Firstly, the energy functional of a general rectangular plate with elastic foundation is calculated. The Rayleigh–Ritz method for investigating the local buckling of unilaterally restrained rectangular plates is applied. The displacement functions and restraining medium are modeled as polynomials and tensionless foundation respectively. The results are obtained for different boundary conditions, aspect ratios and various in-plane compressive and shear loadings. Confirming the validity of this investigation, convergence and comparison studies are undertaken. The comparisons show the efficiency and accuracy of the presented method. It is interesting to note that the unilateral buckling behavior of Functionally Graded Material plates has received far less attention than their Homogenous counterparts. That is why this research attempts to bridge this gap. This research has presented the first-known analysis in the unilateral buckling behavior of rectangular FGM plates with elastic foundation. The results show that the increase of aspect ratios and FGM power index volume decreases the critical buckling load. Also it is demonstrated that the unilateral buckling load is almost constant after increasing the number of bolts over 20. As the increases of bolts distance from the edge of plate, the area surrounded by bolts decreases and thus the local buckling load corresponded to this area increases. On the other hand, as the area between bolts and the edges of triangular plate increase, the local buckling load of this area decreases. Therefore the combination of these two behaviors would result in the total behavior of critical load for the whole area of plate. Additionally, the optimum distance in which the critical load is maximum, as a result plate will be a two behaviors. Keywords: Unilateral restraints, Buckling, Rectangular plate, Functionally Graded Material