This paper presents the design of an optimal Energy Management Strategy (EMS) for a low-cost mechanical-hybrid powertrain. It uses mechanical components only a flywheel, clutches, gears, and a continuously variable transmission for its hybrid functionalities of brake energy recuperation, reduction of inefficient part-load operation of the engine, and engine shutoff during vehicle standstill. This powertrain has mechanical characteristics, such as a relatively small energy storage capacity in the form of the compact flywheel and multiple driving modes to operate the powertrain because of the use of clutches. The optimization problem is complex because it is twofold: (i) to find the optimal sequence of driving modes and (ii) to find the optimal power distribution between the engine, flywheel, and vehicle. Dynamic programming is used to compute the globally optimal EMS for six representative driving cycles. The main design criterion is the minimization of the overall fuel consumption, subject to the systems kinematics, dynamics, and constraints. The results provide a benchmark of the fuel saving potential of this powertrain design and give insight in the optimal utilization of the flywheel system. In addition, the complexity (and computation time) of the problem is reduced by a priori (static) optimization of the power distribution for each driving mode. Static optimization of a dynamic optimization problem yields a sub-optimal solution; however, the results show that the consequences on the fuel saving are small with respect to the optimal one (the difference is <0.8 %).