Humanoid robots walking is still an open challenging problem, where the classic approaches to generate walking motions make use of simple models such as the inverted pendulum or the table cart, combined with the Zero Moment Point (ZMP) criterion. These models allow to generate online motions with feedback corrections. However, they are very conservative and do not allow to exploit the whole-body dynamics of the robot as well as more dynamic walking motions, e.g. often the upper body of the robot does not perform any motion. Whole-body dynamic models are still computationally expensive to be used in an online fashion. However, with a precise description of the dynamic model of the robot, whole-body models have been used to generate feasible and dynamically challenging motions by means of optimal control. The iCub humanoid robot is a child-size robot designed and produced by the Fondazione Istituto Italiano di Tecnologia (IIT). The robot has a special design of Series Elastic Actuators (SEA) in the knee and ankle pitch joints of each leg, which allows to remove the spring, giving the possibility of using both compliant and rigid actuators. In previous works it has been shown that iCub is capable of walking in different environments, by means of simplified models. By means of optimal control and whole-body models with reduced sets of DOF, also motions considering the SEA have been generated for the HeiCub robot. Walking with SEA actuators has been demonstrated to be feasible on the CoMan humanoid robot by means of kinematic primitives. In the present work, instead, we use our approach of motion generation based on optimal control and whole-body models extended to walking on level ground, by formulating a multi-phase optimal control problem considering physical constraints and contact constraints, as well as the dynamic model of the robot both with and without SEA. We apply our method to the reduced version of iCub, HeiCub, located at Heidelberg University, which consists of 15 internal Degrees of Freedom (DOF)