Epicyclic gears, also commonly referred to as planetary gears, are power transfer components that are commonly used in several industrial applications. The structural compliance of thin-rimmed annular ring gear can significantly influence the performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. Therefore to capture the influence associated with ring gear flexibility, the current study will incorporate a finite element-based ring gear formulation into the three-dimensional planetary dynamic load distribution model (Ryali, and Talbot, 2021, “A Dynamic Load Distribution Model of Planetary Gear Sets,” Mech. Mach. Theory, 158, p. 104229). The proposed contact model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several components and system-level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation will be used to study the dynamic response of planetary gear sets where the ring gear is a rotating member. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears.