Aiming at a complex polygonal honeycomb structure,using the virtual work principle,the analytic formulae for a honeycomb core deformation under the small deformation condition were derived by Euler ’s beam model. Then the analytic expressions for equivalent elastic modulus and Poisson’s ratio in two orthogonal directions were obtained and its correctness was validated by numerical simulations. Finally,the effects of wall angles and wall length on the honeycomb stiffness were explored by the analytic expressions. The results show that: the angle θ andφ of walls has a great influence on equivalent elastic modulus and Poisson’s ratio,and the changes of angleθ will lead to positive and negative changes of Poisson’s ratio; the equivalent elastic modulus decreases with the increasing of the length of wall.