Atherosclerosis is one of the most common cardiovascular diseases and is characterized by the gradual accumulation of atherosclerotic plaques in the arteries. This process begins with the infiltration of smooth muscle cells and leukocytes into the intima, leading to the formation of a lipid-rich core separated from the vessel lumen by a fibrous cap. Balloon angioplasty is a common treatment method for restoring normal blood flow in coronary or peripheral arteries affected by atherosclerosis. A critical event during balloon deployment is rupture at the plaque shoulder or at the top of the fibrous cap, depending on the oversizing of the balloon. The mechanical load leading to rupture is strongly influenced by factors such as the geometrical extension of the fibrous cap, the lipid pool, and calcifications. Patient-specific models provide valuable insights; however, they are often limited in their ability to capture the large variability of morphological features that influence the outcomes of balloon angioplasty. To address this gap, we developed an efficient computational model of an atherosclerotic artery that integrates various geometrical features: a healthy three-layered structure, the fibrotic media, the fibrous cap, and the lipid pool. This three-dimensional (3D) parameterized computational model is designed to be easily adjustable to tissue- and region-specific mechanical properties in order to mimic various vessels, such as coronary, iliac, and femoral arteries, as well as different stages of atherosclerosis. In the current study, we employed experimental data from several iliac arteries and fitted these data to the anisotropic Gasser-Ogden-Holzapfel model. Numerous simulations of balloon angioplasty were performed, in which the morphology of the atherosclerotic artery was altered by varying the dimensions of the lipid pool, calcifications, and fibrous cap. Balloon expansion was modeled by explicitly considering the folding and unfolding of the balloon during deployment. The aim of these simulations is to gain deeper insights into the possible causes of damage and plaque rupture during balloon angioplasty under different morphological conditions.