Geometries of arterial cross-sections are extremely diverse from patient to patient, as well as the distribution of their atherosclerotic plaque intrusions. Medical decision on whether a patient has low or high risk of rupture is made on the basis of this information, mostly of geometrical nature. Mechanical models analyzing stress distribution under internal pressure and the corresponding stress concentrations are of great help to support decision making. This is far of being integrated in clinical practice because the conversion of medical images into mechanical outputs of interest is a laborious process. The standard approach to tackle this problem consists in 1) processing the medical image into a segmented geometry, 2) to generate a compliant finite element mesh for the analysis, and 3) to solve the mechanical problem and compute the outputs of interest. Each of three steps is time demanding and jeopardizes the practical and translational use of these tools. The aim of this research is to provide further tools allowing a seamless integration of the full process, minimizing the human intervention and providing robust and reliable computational outputs to support clinical decision making. First, an unfitted approach is devised for this specific case, allowing to encapsulate all the geometrical information in form of level sets supported in a background mesh to be used also in the computation of the mechanical problem. This presents the advantage of precluding the need of a constructing computational mesh, conformal with all the geometrical features of the section and its inclusions. Moreover, this approach paves the way for a using Reduced Order Models (ROM) and therefore to drastically accelerate the computation. Nevertheless, the variability of the arterial cross-sections is a serious drawback for using ROM. The elements of the training set (snapshots) are too diverse to extract common features, and the new elements to be analyzed have little in common with the database from which the ROM has learned. The work contributes to shape the mechanical problem statement with new boundary conditions, to provide insightful analysis of the dispersion of the observed different geometries, to devise a specific unfitted approach, and to test the ROM strategy in this scenario.