The ball bearings that form part of mechanisms in space applications are subjected to vibrations. The result of these vibrations is gapping between the rings of the bearing. This gap allows collisions of the ball with the races, which produce high contact stresses. These high stresses can cause indentation damage on the ball and the raceways, and may lead to malfunction of the bearing, and therefore the mechanism the bearing forms a part. Previous studies have develop a 2-DOF model in order to predict gapping using for the calculation, the bearing stiffness predicted by a computer software called CABARET, with satisfactory results. In the present study the model optimized, as the comparison with available measured gapping values verifies, by the introduction of the non-linear stiffness to the existing prediction model. A method of contact stress prediction developed, based on the analysis of the collisions between the ball and the rings of the bearing, considering the laws of conservation of energy and the laws of motion, involving evaluations of the closing velocity, the collision acceleration and the impact force. Comparison of the Hertzian stress predicted by the author showed better agreement to experimental indentation damage (made by another investigator), than the CABARET predicted stress.