A simulation model of a two mode power-split hybrid electric vehicle (HEV) is proposed in this paper for the purpose of HEV dynamics analysis and control system design. The bond graph methodology is used to model dominant dynamic effects of the mechanical part of the HEV transmission. Simple quasi-static battery model, the environment model, the tire and the power losses model of a vehicle are included, as well. A low-level electric generator speed control loop is designed, which includes a PI controller tuned according to the symmetrical optimum tuning procedure. Finally, off-line optimization by conjugate gradient-based BPTT-like optimal control algorithm, which is based on the presented mathematical model, is also given in the paper.