A typical control-oriented automatic transmission model does not include some mostly nonlinear effects such as transmission component friction and backlash, Stribeck clutch friction, clutch drag, and engine block dynamics. It is shown in this paper that such a model cannot provide an accurate description of the power train dynamics during park/reverse and park/drive engagements. An analysis of the influence of various nonlinear effects on the engagement dynamic behavior is presented. The relevant nonlinear effects are incorporated in the basic power train model. The extended model is experimentally validated for typical engagement operating modes.