In many machines and mechanical components, there is a need for new bearing technologies to reduce friction and wear, and provide precision control of motion when the load is varied. This can be provided by electronically controlled actuators and sensors on the surfaces, but then the system reliability can be an issue. In contrast, biomimetic surfaces can be created that adapt mechanically to variations in load. This work uses numerical methods to research the use of self-adapting surfaces for bearings that are based on the deformable nature of biological materials such as articular cartilage. These surfaces are designed to change their profiles to achieve a desired behavior, without any external control. The surfaces change their profile to control the film height and tilt of the bearing to a near constant value for different loads. If the surfaces are tilted, the grooved self-adapting surfaces will also react with a larger restoring moment than a conventional grooved surface. These surfaces could be beneficial to applications where electrical systems and controls are not feasible.