Abstract: The column supported plate structure is a very common floor system. The accurate solution on the internal forces in the plate has not been attempted. The bending problem of a rectangular plate is assumed to be generalized statically determinate or generalized statically indeterminate. For the former, the column supports are replaced by the supporting reactions which are calculated using static equilibrium. The plate supported by columns is viewed as a plate with four free edges subjected to the original loads and the supporting reactions. The general solution of deflection which satisfies the free boundary conditions is used. Composite particular solutions are used that satisfy the equilibrium differential equation, the shear force conditions on the free edges and the concentrated force conditions at the points where columns are located. The internal forces of plate can be solved for directly using boundary conditions at four edges of the plate and the deformations of the column supports. For the generalized statically indeterminate case they are solved for using the superposition principle. The solution is effective for bending of the plate supported by columns at arbitrary locations under arbitrary loads and has the advantage of high accuracy that is proved by inverse analysis examples.