This paper presents the design and the experimental validation of a Series rotary Elastic Actuator (SEA). The actuator is conceived to be installed on both the knee and the ankle joint of the version three of the humanoid robot iCub. The actuator is composed of an electric motor, a gearbox, and a customized torsion spring. The stiffness value of the torsion spring is the outcome of an optimisation problem that considers several criteria, e.g., the maximum readable torque from the SEA and the total stiffness of the mechanism. Then, the synthesis of the elastic element exploits a Finite Element Method (FEM), which allows us to meet the requirements. Experiments on the conceived design have been performed on a custom set-up, and they verify the match between the desired and real value of the mechanism stiffness with a maximum resultant error of 9%. An estimation of the damping associated with the SEA is also performed during experimental validation.