A control-oriented model of a typical four-speed automatic transmission is developed by using the bond graph modeling method. The planetary gear set model utilizes the Karnopp friction model for hydraulic and one-way clutches, in order to provide a favorable computing efficiency. The full gear set model is reduced for various phases of the park/ reverse and park/drive engagements. The reduced gear set models and linearized torque converter model are used as a basis for an algebraic analysis of the engagement dynamics. The analysis is originally conducted for the basic case of fully applied brake, and it is then extended by an analysis of the influence of wheel dynamics in the brake-off case. The analysis results are verified by computer simulations and experiments.