Hip replacement surgery is one of the most common procedures in the world. Annually, more than 1 million hip replacement surgeries are performed worldwide, while it is anticipated that this number will double in the next decade. After the damaged or worn out hip joint is replaced with the artificial hip joint, bone healing process starts. In order to ensure the long and proper function of the artificial joint, the connection between the bone and the inserted implant should be as strong as possible. However, if the established connection is not strong enough, the implant starts to loosen. Experimental studies have indicated that implants with a rough surface form a stronger connection with a bone. The goal of this paper was to numerically analyze different spherical shapes on the implant surface. The results obtained numerically are considered to be a very helpful addition to the experimental studies. Numerical analysis of the implant surfaces has been performed using the Finite Element Method. The obtained results include distribution of the shear stress on the implant surface. This type of stress is important for this study because in order to promote bone ingrowth, the shear stress should be minimized. Our study considered the interaction between cortical bone and implant with rough surface. Material properties and boundary conditions were adapted from literature.