A thorough understanding of the diseased tissue state is necessary for the successful treatment of a blocked arterial vessel using stent angioplasty. The constitutive representation of atherosclerotic tissue is of great interest to researchers and engineers using computational models to analyse stents, as it is this in silico environment that allows extensive exploration of tissue response to device implantation. This paper presents an in silico evaluation of the effects of variation of atherosclerotic tissue constitutive representation on tissue mechanical response during stent implantation. The motivation behind this work is to investigate the level of detail that is required when modelling atherosclerotic tissue in a stenting simulation, and to give recommendations to the FDA for their guideline document on coronary stent evaluation, and specifically the current requirements for computational stress analyses. This paper explores the effects of variation of the material model for the atherosclerotic tissue matrix, the effects of inclusion of calcifications and a lipid pool, and finally the effects of inclusion of the Mullins effect in the atherosclerotic tissue matrix, on tissue response in stenting simulations. Results indicate that the inclusion of the Mullins effect in a direct stenting simulation does not have a significant effect on the deformed shape of the tissue or the stress state of the tissue. The inclusion of a lipid pool induces a local redistribution of lesion deformation for a soft surrounding matrix and the inclusion of a small volume of calcifications dramatically alters the local results for a soft surrounding matrix. One of the key findings from this work is that the underlying constitutive model (elasticity model) used for the atherosclerotic tissue is the dominant feature of the tissue representation in predicting tissue response in a stenting simulation.