Modern planetary automatic transmissions are complex reconfigurable dynamic systems. Appropriate mathematical models will enhance the understanding of shift dynamics, the effort of the hardware design optimization, and the efficiency of software development and calibration. This paper focuses on the bond graph model based method for modeling the transmission dynamics. We first summarize bond graph models for the most relevant planetary gear sets (single, double and stepped pinion and Ravigneaux). We then demonstrate how to use these building blocks to construct device-mapping bond graph models of complete planetary transmissions of 6 speed and 10 speed transmissions for RWD. We further describe the procedure of deriving mathematical models based on derived bond graph models. The case with all clutches slipping is considered first and then cases with some clutches locked for so-called reduced order models. As an alternative for derivation of numerical reduced order model we propose a method based on linear algebra manipulations. We also demonstrate how the device-mapping bond graph model can be converted into a conceptual torque-path bond graph for engagements and multi-element shift events, similar to the generic bond graph for a conventional two-element shift shown in prior literature. Finally, we provide a qualitative analysis of effective rotational inertias and shift dynamics.