In this paper we apply the artificial compressibility method (ACM) in strongly coupled fluid-structure interaction (FSI) computation of blood flow in an elastic artery. Previously published and here referred to as the ACM/FSI method uses the idea of artificial compressibility by Chorin 1967, except the term of pressure time derivative in the continuity equation is used to mimic the response of the walls, thereby stabilizing the iterative coupling. To reach the aim, we present a new way, the test load method, to improve ACM/FSI computations. In the test load method, the compressibility parameter is computed locally and is based on the mesh deformation of the fluid domain. The functionality of the ACM/FSI coupling with the test load method is demonstrated in an arterial flow simulation, and the combination is shown to provide a robust convergence. In order to get the test cases to correspond better to human physiology, one-dimensional FSI models are combined with the higher dimensional test models.