Relaxation and successive approximation methods are used to solve Von Karman's equations as applied to initially flat, rectangular plates with large deflections under either normal pressure or combined normal pressure and side thrust, and several specific cases are analyzed. The general method developed may be applied to bending and combined bending and buckling problems with practically any boundary conditions to any required degree of accuracy or applied to solve the membrane theory of the plate which applies when the deflection is very large in comparison with the thickness of the plate.