A mathematical model to simulate human walking motions and study the dynamics behind walking is developed which is adjustable to accommodate different cases such as the single and double support phases of walking. We first propose a technique for estimating joint moments and position coordinates of body segments using the method of inverse dynamics. The estimates are then used as initial joint torques for solving the model as an optimal control problem with the setup of appropriate objective functions and constraints. Numerical experiments on the developed model and solution technique have been performed and the numerical results show that the model is able to replicate human walking motions and the optimal joint torques can be calculated to produce the resulting motions.