Studying the solid mechanics of angioplasty provides essential insight in the mechanisms of angioplasty such as overstretching the disease-free tissue, plaque disruption or dissection, redistribution inside the wall and lipid extrusion etc. We desribe our current understanding of the mechanics of angioplasty based on the example of a human iliac artery with an eccentric stenosis. We outline a new approach which has the potential to improve interventional treatment planning, to predict the balloon and stent-induced wall stresses as well as the dilation success. In particular, we use MRI to obtain accurate geometrical data for the vessel wall and plaque architecture and to identify their different types of soft (biological) tissues and calcifications. One issue is to characterize the quasistatic stress-strain response of these components in both axial and circumferential directions. We present new experimental results showing strong nonlinearity and anisotropy. Another issue is to identify predominant directions of each component by analyzing orientations of cellular nuclei. The morphological and mechanical information is used for the elastoplastic constitutive model designed to capture the finite strains of the stenotic artery during angioplasty. The three-dimensional model is fitted to the experimental data. Associated material parameters, corresponding to the different tissues of the stenosis, are presented. The numerical part outlines briefly the concept of the finite element model and, based on a computational structural analysis, discusses the mechanism of angioplasty for the considered type of stenosis.