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Purpose - The purpose of this paper is to present a computational framework for the simulation of patient-specific atherosclerotic arterial walls. Such simulations provide information regarding the mechanical stress distribution inside the arterial wall and may therefore enable improved medical indications for or against medical treatment. In detail, the paper aims to provide a framework which takes into account patient-specific geometric models obtained by in vivo measurements, as well as a fast solution strategy, giving realistic numerical results obtained in reasonable time. Design/methodology/approach - A method is proposed for the construction of three-dimensional geometrical models of atherosclerotic arteries based on intravascular ultrasound virtual histology data combined with angiographic X-ray images, which are obtained on a routine basis in the diagnostics and medical treatment of cardiovascular diseases. These models serve as a basis for finite element simulations where a large number of unknowns need to be calculated in reasonable time. Therefore, the finite element tearing and interconnecting-dual primal (FETI-DP) domain decomposition method is applied, to achieve an efficient parallel solution strategy. Findings - It is shown that three-dimensional models of patient-specific atherosclerotic arteries can be constructed from intravascular ultrasound virtual histology data. Furthermore, the application of the FETI-DP domain decomposition method leads to a fast numerical framework. In a numerical example, the importance of three-dimensional models and thereby fast solution algorithms is illustrated by showing that two-dimensional approximations differ significantly from the 3D solution. Originality/value - The decision for or against intravascular medical treatment of atherosclerotic arteries strongly depends on the mechanical situation of the arterial wall. The framework presented in this paper provides computer simulations of stress distributions, which therefore enable improved indications for medical methods of treatment. © Emerald Group Publishing Limited.