In order to increase the aerodynamic performances of their engines, aircraft engine manufacturers try to minimize the clearance between rotating and stationary parts in axial and centrifugal compressors. Consequently, the probability of contact increases, leading to undesirable phenomena caused by forced excitation of the natural modes or by modal interaction. Due to the complexity of these phenomena, many numerical studies have been conducted to gain a better understanding of the physics associated with them, looking primarily at their respective influence on potential unstable behaviors. However, the influence of other physical phenomena, such as friction and wear, remains poorly understood. The aim of this work is to show some effects associated with friction and wear on the dynamic behavior resulting from blade-to-casing interaction. The numerical study reported here is based on a simplified finite element model of a rotating bladed disk and a flexible casing. The contact algorithm uses an explicit time marching scheme with the Lagrange multipliers method. Friction and wear are formulated using, respectively, Coulomb's and Archard's laws. The rotational speed is set to critical speed giving rise to modal interaction between a backward mode of the casing and a counter-rotating mode of the bladed disk with one nodal diameter (ND). Contact is initiated by a dynamic excitation of the stator. In the presence of friction, the system becomes unstable when a sideband of the excitation frequency coincides with 1ND mode of the bladed disk. The introduction of wear leads to a vibration reduction, while the abradable material is removed by the wear process. The number of wear lobes produced on the casing is related to the ratio between the vibration frequency of the blades and the rotating speed. The ratio obtained by means of the FE model corroborates experimental observations.