Abstract Based on three-dimensional theory of elasticity, semi-analytical solutions for free vibration of cross-ply laminated cylindrical panels are derived applying the state space approach (SSA) and discrete singular convolution (DSC) algorithm. One pair of opposite edges are assumed to be with simply supported and the other pair of edges arbitrary boundary conditions. The thickness direction of panels is chosen as the transfer direction in SSA, and the DSC is employed to discretize the axial direction of panel. Hence, the original partial differential equations are transformed into a state equation consisting of first-order ordinary differential equations. The application of DSC can deal with various boundary conditions, which cannot be solved in the conventional SSA. Accuracy and convergence for laminated cross-ply panels are validated through numerical examples.