The pericyclic drive is characterized by very high single stage gear ratios (~50:1). This is enabled by nutational motion kinematics, load sharing over many teeth (~10% of teeth), and high power density capabilities. A novel methodology for loaded tooth contact and mesh stiffness analysis of an internal - external straight bevel gear pair, with a difference of 1 or 2 teeth, meshing at small shaft angles (2° - 5°) in this non-conventional transmission is described. A computationally fast algorithm to generate modified external bevel gear with profile and lead crowning was developed to localize bearing contact. Thereafter, an efficient nearest neighbor search algorithm was used to find contact points. Load distribution was calculated by minimizing the total elastic potential energy during meshing. Finite Strip Method (FSM) was applied to accurately calculate tooth deflection for non-standard gears in point contact. Further, maximum bending stress has been formulated as a useful tool for designers by curve fitting the results from several Finite Element (FE) simulations. Results from FE analysis are also used to validate contact stress and gear tooth deflection solutions. The results also show that mesh stiffness variation is small (10 - 15%). Therefore, lower mesh excitation and gear noise can be expected in a Pericyclic drive.