Nonlinear analysis of a structure that includes two connected circular and annular thin plates under uniform loads has been performed by shooting method. Plates are connected by linear tensional spring. The von Karman equations with corresponding boundary conditions (clamped-clamped) have been solved by employing parallel shooting method. The variation of displacements, bending and membrane stresses of plates under variety of loading intensity are obtained. Finally the variation of maximum stresses due to different parameters such as spring tensional rigidity, plates thickness ratio and ratio of annular inner radius to circular outer radius are considered