Composite plates are designed in order to maximize the performance with respect to eigenfrequencies. The plates are considered to be laminates where the individual plies consist of orthotropic material. The design task is the orientation of the orthotropic material in each element of the discretization and the ratio between the amounts of material put in the two directions of the fiber-net. The optimizations are performed using the finite element method for analysis and the optimization approach is a two-step method. In the first step we first find the best design on the basis of a recursive optimization procedure based on an optimality criterion (OC). In the second step mathematical programming (MP) and sensitivity analysis are applied to find the final optimized design.