A novel formulation of the differential equations governing the flow of viscoelastic fluids is proposed, based on the use of the traceless stress tensor (TST). It is shown that it naturally leads to the appearance of a modified viscosity given by eta + (lambda /3) . tr(tau) where eta is the shear-viscosity coefficient, lambda the relaxation time and tr(tau) the trace of the extra stress tensor. This modified viscosity reaches high values near singular points, the troublesome regions when solving numerically the equations, and therefore its inclusion will tend to stabilise the computations when the modified-viscous terms in the momentum equations are treated implicitly.