A new mixed finite element method for computing viscoelastic flows is presented. The mixed formulation is based on the introduction of the rate of deformation tensor as an additional unknown. Contrary to the popular EVSS method [D. Rajagopalan, R.A. Brown and R.C. Armstrong, J. Non-Newtonian Fluid Mech., 36 (1990) 159], no change of variable is performed into the constitutive equation. Hence, the described method can be used to compute solutions of theological models where the EVSS method does not apply. The numerical strategy uses a decoupled iterative scheme as a preconditioner for the GMRES algorithm, The stability and the robustness of the method are investigated on two benchmark problems: the 4:1 contraction flow problem and the stick-slip flow problem. Numerical results for the PTT [N. Phan-Thien and R.I. Tanner, J. Non-Newtonian Fluid Mech., 2 (1977) 353] and the Grmela [J. Grmela, J. Rheology, 33 (1989) 207] models show that our method is remarkably stable and cheap in computer time and memory.