Sandwich panels are widely used in the aerospace industry instead of solid plates due to their high flexural stiffness-to-weight and flexural strength-to-weight ratios. However due to the mismatch of properties between the face sheets and the core, stress concentrations can occur at the face sheet/core interfaces, often leading to delamination. One possible solution to this problem is the introduction of a graded core - a core in which the properties vary gradually from the face sheets to the core centre, eliminating any abrupt changes in properties. In this paper a 3D finite element method, fully validated through comparison with results from the literature and a 3D elasticity solution, is applied to modelling of sandwich panels with graded core. The approach makes use of graded elements to study the effect of varying the boundary conditions on the elastic deformation of the panel subject to uniformly distributed loading. Comparative analysis of stress and displacement fields in sandwich panels with homogeneous and graded cores is carried out under various combinations of simply supported, clamped and free edges.