The present paper deals with the static analysis of a novel biped walking and climbing robot, which is provided of a serial-parallel leg mechanism with 6 d.o.f.s, since composed by two 3-RPS parallel modules. Twelve electromechanical linear drives are foreseen to actuate the prismatic joints of both leg mechanisms. Thus, the static analysis of the biped robot is proposed by considering the worst configurations for the walking stability of the robot, during its lateral and forward motions. A specific algorithm for the static analysis of the 3-RPS parallel module is reported and related to the biped robot walking stability, along with first numerical results and validation.