The influence of viscoelastic effects on blood flow in large arteries is studied numerically. The description of the blood flow uses the conservation of mass and momentum and a constitutive relation of Jeffreys' type (Oldroyd-B) and appropriate relations to describe the shear thinning behaviour. The steady flow studies are carried out in an axisymmetric tube with a local constriction modelling a stenosed blood vessel and in a three-dimensional 90 degrees curved tube. The numerical approach applies a decoupled technique where the computation of kinematics and stresses is separated. The governing equations are solved by means of an upwind stabilised Galerkin finite element method. The numerical results indicate significant influence of viscoelastic effects in the stenosed model. The flow through the curved tube shows minor quantitative viscoelastic influence. The influence of the shear thinning effect can be observed in both geometries. The results demonstrate that the viscoelastic behaviour of the local flow patterns in large arteries is dependent on the shape of the flow domain.