Handling cache related preemption delay (CRPD) in pre-emptive scheduling context for real-time systems stays an open issue despite of its practical importance. Priority assignment algorithms and feasibility tests are usually based on the assumption that the preemption cost is negligible. Then, a system that could be schedulable on design time can fail to meet its timing constraints in practice due to preemption costs. In this article, we propose a simple approach to take into account the CRPD when performing priority assignment. The goal is to have a priority assignment algorithm which guarantees the schedulability of systems when tasks suffer CRPD on run-time. For such a purpose, we propose an extension of the feasibility test of Audsley and illustrate it with some examples. An implementation of our priority assignment method has been integrated to the Cheddar scheduling analyzer. A comparison of the proposed algorithm with classical priority assignment algorithms is achieved.