The boundary element method (BEM) is already a well-established numerical technique to deal with an enormous number of complex engineering problems. Some features of this method is, modeling a variety of infinite and intricate environments, less primary input data, high processing speed and more computational accuracy. Depending on the capabilities of BEM, some scientists have used this method to analyze the problems of the plates. In this thesis, the bending analysis of thin elastic plate with direct BEM is studied. The applied method is not restricted to specific plate shapes or boundary conditions and it is formulated in terms of boundary quantities, which have direct physical meaning, namely the transverse displacement, the normal slope, the bending moment and the equivalent shear force. The integral representation of the solution of the plate equation in terms of these boundary quantities is based on the generalized Rayleigh-Green identity. The evaluation of the deflection at a point in the interior of the plate requires that the values of boundary quantities be known. As regards only two of the four boundary quantities can be prescribed, two coupled boundary integral equations are formulated to determine the two unknown quantities on the boundary. According to the numerical techniques, the boundary of plate is divided to a certain number of constant element and a system of linear equations is constituted based on boundary integral equations. The boundary variables are assumed to be constant along each boundary element. The corner effects and their treatment in the numerical procedure are also discussed. After solving the system of linear equations using Gauss elimination method according to the boundary conditions of problem, the boundary quantities will be known. Moreover, the stress resultants at a point in the interior of a plate are obtained with differentiation of some specified integral equations. Several computational examples concerning plates with diverse shapes are presented. Bending analysis of a thin rectangular plate with different boundary conditions are studied and convergence of results are shown in several charts based on various number of boundary elements. In other examples the bending of triangle, parallelogram, trapezius and sektor plates are discussed. The results show good agreement with analytical and ?nite element results available in the literature. Key Words: Boundary element method, thin elastic plate, generalized Rayleigh-Green identity, Boundary integral equations
