It has been discussed some time that in optimal design of plate with thickness as design variable, many thin ribs appear and optimal solution is very mesh sensitive. To prevent this difficulty, the expansion (relaxation) of the solution space is done so as to include microstructure, and structural optimization can be carried out as the optimal distribution problem of the microstructure, which include layout optimization as well as shape optimization. Formulation of plate equation for the plate with rapidly varying thickness is derived using homogenization theory, under the assumption of Y-periodicity. The optimization is formulated as minimize mean compliance under constraint on the total volume of material to be used. Using this method, the optimal shape and layout of plate structures were obtained and it was shown that in statically indeterminate plate structures the hinge lines appear in the optimal solutions, which is distinct in plate structures.