Abstarct: In this thesisthe buckling of homogeneous and isotropic rectangular plates with centrally located cutout is studied. The plate is initially perfect and it has finite dimensions and the effect of circular and square cutouts with different sizes on the buckling load is investigated. The buckling load is presented for different combinations of free, clamped and simply supported boundary conditions at the plate outer edges and for different aspect ratios.The buckling load is calculated in two steps: solving the equations ofthe initial state of equilibrium and using the obtained results to solve the stability equations. The buckling load calculation is performed for three different cases: a rectangular plate without cutout under non-uniform in-plane loading, annular plate and rectangular plate with circular and square cutouts in the center. In a rectangular plate under in-plane loading, the existence of cutout changes the distribution of stress field. This stress field must satisfy the boundary conditions at the cutout edges and also at the plate edges. In this thesis two solutions are presented for this problem. In the first solution the stress field is calculated by using the complex potential functions and domain mapping. The second solution is baxsed on the harmonic expansion of stress function in polar coordinates. In both solutions, the boundary condition at the plate edges is applied by using an integral which is derived from the virtual work method and it is called the boundary integral. As a result, the obtained solution satisfies the boundary condition at the cutout edges exactly and the boundary conditions at the plate edges with good accuracy. After calculating the prebuckling stress field, the stability equations have to solve to obtain the buckling load and mode shape. In the annular plate and for the axisymmetric case, the perturbation technique is used to solve the stability equations and for the non-axisymmetric case, the ringing method is used to solve these equations. In a rectangular plate with cutout, the prebuckling stress components are too complicated and as a result the Ritz energy method is used for buckling load calculation. In this method the out of plate displacement components are approximated by admissible functions representing the lateral vibration mode shapes of a beam. The buckling load is calculated for different uniform and non-uniform loadings, boundary conditions and cutout sizes. The solution method is validated by comparing the results with numerical solution baxsed on the finite elementmethod and also with other references.