We determine numerically eigenfrequencies of sounding boards of a classical guitar. As a model of sounding board we use a pre-stressed thin plate. Triangular finite elements are applied. Finite element relationships are constructed on the basis of mixed variational Reissner approach and independent approximation of displacements and deformations. Wood is considered as natural fibrous composite material. The validation of the numerical model is justified by the study of convergence. Data obtained are in good agreement with known analytical results. We investigate the relationship between eigenfrequencies and eigenmodes, on the one hand, and boundary conditions at the edge, on the other hand.