Implant loosening is one of the most important modes of failure of cemented total hip replacement. It may be related to the cement strength, cement-prosthesis interface, cement-bone interface, surgical technique, or stem design. The main purpose of this study is to investigate the effect of bone-cement interface mechanical properties on cement degradation. The computational methodology proposed herein combines a previously developed bone-cement interface damage model and an accumulative damage model for bulk cement. This has been applied to a finite element model of an Exeter cemented hip implant. A higher strength of the bone-cement interface due to a higher amount of interdigitated bone results in faster cement deterioration. Over time, damage both at the bone-cement interface and in the cement mantle worsens. Also, a larger debonded area was predicted proximally, as observed in clinical practice. We conclude that the computational model proposed herein allows a realistic simulation of the bone-cement interface debonding and cement degradation, being a useful tool in the design of this kind of medical devices.