A traceless variant of the Johnson-Segalman viscoelastic model is presented and applied
to blood flow simulations. The viscoelastic extra stress tensor is decomposed into its
traceless (deviatoric) and spherical parts, leading to a reformulation of the classical
Johnson-Segalman model. The equivalence of the two models is established comparing model
predictions for simple test cases. The new model is validated using several 2D benchmark
problems, designed to reproduce difficulties that arise in the simulation of blood flow in
blood vessels or medical devices. The structure and behaviour of the new model are
discussed and the future use of the new model in envisioned, both on the theoretical and
numerical perspectives.