Purpose: Residual stress has a great influence on the mechanical behaviour of arterial wall. Numerous research groups used the Uni-form Stress Hypothesis to allow the inclusion of the effects of residual stress when computing stress distributions in the arterial wall. Nevertheless, the available methods used for this purpose are very computationally expensive, due to their iterative nature. In this paper we present a new method for including the effects of residual stress on the computed stress distribution in the arterial wall. Methods: The new method, by using the Uniform Stress Hypothesis, enables computing the effect of residual stress by averaging stresses across the thickness of the arterial wall. Results: Being a post-processing method for the computed stress distributions, the proposed method is computationally inexpensive, and thus, better suited for clinical applications than the previously used ones. Conclusions: The resulting stress distributions and values obtained using the proposed method based on the Uniform Stress Hypothesis are very close to the ones returned by an existing iterative method.