Numerical and analytical studies on cylindrical geometries have shown the relevance of accounting for residual stresses in arterial modeling. However, multiple difficulties, both geometrical and numerical, arise when enforcing residual stresses in patient-specific arteries. This is the reason of the few simulations that have been developed on this kind of geometries. In this paper we present a methodology that allows to include residual stresses in arbitrary geometries. Since it is not necessary to know the opened configuration of the artery, it makes it possible to take advantage of non-invasive image acquisition techniques such as CT or MRI to create customized arterial models. A simplified initial strain field showing its accuracy when applied to actual in vivo closed geometries is hypothesized from an opening angle experiment. In addition to residual stresses, the anisotropic hyperelastic and multilayered nature of the arterial tissue was accounted for the simulations of the behavior of a human coronary and iliac arteries. Results show the relevance of considering all these features for getting realistic results and the relative accuracy of using approximate solutions of residual stresses in patient-specific arterial simulations.