Modifications and improvements to conventional state space differential quadrature method are proposed for free vibration analysis of thick, soft-core sandwich panels with arbitrary edge boundary conditions, using an exact two-dimensional elasticity model. The modifications are based on a systematic procedure to implement all possible combinations of edge boundary conditions including simply supported, clamped, free and guided edges. Natural frequencies and mode shapes are obtained and compared with exact elasticity solutions from state space method and approximate solution from finite element simulations; demonstrating the high numerical accuracy and rapid convergence of the modified method. Further, the proposed framework is compared to the conventional implementation of the state space differential quadrature method for thick cantilever sandwich panels and is shown to give results with better accuracy and faster convergence. © The Author(s) 2017.