In the building of industrial systems, for the purpose of reinforcing these systems, other plates are usually attached to the side plates as reinforcing plates. For example, plates attached to the foundations, connections of mechanical components, beam reinforcing plates and concrete columns can be named. Steal sheets connected to the side of concrete filled beams causes the increase in the resistance of the beams against the applying external forces. Applying external forces to the concrete beams causes compression, bending and shearing stress in these plates which in turn cause local buckling and eventually instability of the plates. Also, studying and accurate analysis of their behavior seem inevitable along with the advancement techniques of the production of composites, which mainly play the role of reinforcing the industrial systems. In modeling the behavior of these plates, the foundation acts as a unilateral flexible foundation. The surface of the flexible foundation prevents two different aspects of buckling behaviors of the plates and causes a special kind of buckling named “unilateral buckling”. In the present thesis, analyzing the unilateral local buckling of thin rectangular plates are investigated by creating abrupt changes in the thickness of the plates on the unilateral flexible foundation by means of Reyleigh-Ritz and finite element methods. In the Reyleigh-Ritz method, the displacement field is selected by means of harmonic polynomial fields with boundary conditions. In the Finite Element Method, quadrilateral four-node element with 12 freedom-degree is used for the out-of-plane, and 8 freedom-degree for in-plane solutions. The surface of connection, like a unilateral flexible foundation, which shows resistance only in one direction, becomes our model. The above methods are appropriate for computer calculations and the effect of coefficients for the unilateral and bilateral compress buckling, bending and shearing on various reinforcing situations, hole and various plate dimensions are presented in tables and interaction curves. Also, thesis results are compared with the results of past research-which had been done without reinforcing plates—and the correctness of the numerical methods have been verified. Key Words Reinforcing plates, Reyleigh-Ritz, finite element, unilateral flexible foundation, unilateral local buckling.