Smoothed Particle Hydrodynamics (SPH) simulations of elastic solids and viscous fluids may suffer from unphysical clustering of particles due to the tensile instability. Recent work has shown that in simulations of elastic or brittle solids the instability can be removed by an artificial stress whose form is derived from a linear perturbation analysis of the full set of governing SPH equations. While a linear analysis cannot be used to derive the corresponding form of the artificial stress for a viscous fluid, here we show that the same construction which applies to elastic solids may also work for viscous fluids provided that the constant parameter entering in the definition of the artificial stress is properly chosen. As a suitable test case, we model the formation of a circular van der Waals liquid drop and show that the tensile instability is removed when an artificial viscous force and energy generation term are added to the standard SPH equations of motion and energy, respectively. The optimal value of the constant is constrained by the ability of the model simulation to reproduce both a sufficiently smoothed density profile and the van der Waals phase diagram.