In this paper we extend our previous work on solving the inverse kinematics problem for a humanoid robot in general multi-contact stances under physical limitations and static equilibrium constraints, to the case in which the contact is made on a non-rigid deformable environment support. We take a finite element approach to solve the static equilibrium equations for the system made of the robot and the deformable support within the linear elasticity model. Example simulation results show the humanoid robot HRP-2 taking contact support with hand or foot link on a deformable cube.