Abstract: A new hybrid finite volume method for the numerical simulation of oldroyd B fluid flows is presented.As main features of this method,the technique of Chorin s pseudo compressibility is used to solve the 3-D steady incompressible continuity equation and momentum equations and the streamline upwinding approach is used to discretize the constitutive equations.The method has dealt with a sudden contractions viscoelastic flow problem for a range of Weissenberg numbers.Numerical results obtained are in good qualitative agreement with existing exprimental ones.