A mathematical model was firstly built for investigating the contact deformation distribution in a wire race ball bearing. The numerical computing program was developed in MATLAB ® , by employing an example of a wire race ball bearing with a 1000 mm diameter used in a large-scale caterpillar disaster relief robot. The contact deformation distribution in the elliptical contact zone of the wire and the ball was obtained. The finite element simulation was carried out to demonstrate the validity of the mathematical model and numerical method. It shows that the results by the numerical method are in good agreement with those by the simulation. The present work provides a significant support for studying the stiffness of the wire race ball bearing, and for boosting the application in the large scale rescue robot.