SUMMARYThe title problem is investigated using the differential quadrature method based on the state-space formalism. The plates, with mixed boundary conditions, may cross over one-way internal rigid line supports that impose zero transverse displacement constraints. Differential quadrature procedure is applied in the direction of line supports, while exact solution is sought in the transfer domain perpendicular to the line supports using the state space method. To avoid numerical instability in the transfer matrix method, joint coupling matrices are introduced, mainly according to the continuity conditions at line joints. Natural frequencies of rectangular Kirchhoff plates with general boundary conditions are calculated and compared with the results from other methods. Effects of location of internal line supports and the mixed boundary conditions on the frequency parameters are discussed.