In recent years, internal gears are used commonly in a number of automotive and aerospace applications especially in planetary gear drives. Planetary gears have many advantages such as compactness, large torque-to-weight ratio, large transmission ratios, reduced noise and vibrations. Although internal gears have many advantages, there are not enough studies on it. Designing an internal gear mechanism includes two important parameters. The gear mesh stiffness which is the main excitation source of the system. In this paper, 2D gear models are developed in order to compute gear mesh stiffness for various rim thicknesses and different rim shapes of the internal gear design. Effects of root stress with varying rim thickness and some tooth parameters are investigated by using 2D gear models. The stress calculated according to ISO 6336 and the stresses calculated against FEM are compared. These results are well-matched. It is observed that when the rim thicknesses are increased, both the maximum bending stresses and gear mesh stiffness are decreased considerably.