In this paper we present a new strategy for obtaining blood vessel tissue prestress for use in fluid–structure interaction (FSI) analysis of vascular blood flow. The method consists of a simple iterative procedure and is applicable to a large class of vascular geometries. The formulation of the solid problem is modified to account for the tissue prestress by employing an additive decomposition of the second Piola–Kirchhoff stress tensor. Computational results using patient-specific models of cerebral aneurysms indicate that tissue prestress plays an important role in predicting hemodynamic quantities of interest in vascular FSI simulations.