Abstract : Numerical simulations of non-newtonian fluids such as wormlike micellar solutions in confined geometries are of great interest in the oil industry. Their main property called shear-banding is a brutal transition from a very viscousstate to a very fluid state above a certain threshold value of shear stress. This feature leads to a very complex behavior in 3D flows. A modified version of the Johnson-Segalman’s model, adapted to our situation (flows with a strong extensional component) is presented. A particular attention is paid to inlet and outlet boundary conditions, and a Poiseuillelike submodel is derived in order to get natural velocity and stress profiles that can be used at the boundaries. A numerical method is then developed, and stability issues are presented. Our results show the interest of the modified Johnson-Segalman’s model performed in this article. A set of 3D numerical simulations are then presentedin order to understand the influence of the junction geometry upon the jamming effects observed in the behaviour of this kind of fluids.