Aluminum honeycomb core is one of the most sought after material for the sandwich panel for light weight applications. While the aluminum face sheet is isotropic, the honeycomb core assumes orthotropic characteristics due to its configuration and strenuous load transfer paths. It is now well established that stiffness, dynamic, and low velocity impact response of the honeycomb core sandwich panel are critically dependent on the elastic constants of the core. An attempt is made to determine the elastic constants of orthotropic core through finite element approach simulating the load transfer and fixity boundary conditions likely to be prevalent in the unit cell of the honeycomb core. The cell wall thickness and the cell shape dictated by plastic bending limitations have also been simulated to determine their influence on the elastic constants. Further, the cell wall thickness and the bend radius have been varied and their influence on orthotropic elastic constants has been determined. The results of the study have been compared with analytical solutions proposed by researchers. The finite element procedure evolved is a simple, efficient, and quick solution methodology to accurately predict elastic constants of honeycomb core depicting the exact cell size and shape.