Steady state evaporation from a planar liquid surface into vacuum is modelled by non-equilibrium molecular dynamics simulations of a Lennard-Jones fluid. Studies are made for liquids at a low temperature T/T-c = 0.53, a medium temperature T/T-c = 0.65 and a high temperature T/T-c = 0.84, where T-c is the critical temperature. Results are given for the profiles of density, kinetic temperature, distinguishing between its components, and drift velocity, for the outgoing, incoming and total particle flux as well as for the evaporation coefficient alpha. Moreover, velocity distribution functions are shown. The simulation results are compared with those from kinetic theory. The key findings are: (a) For the low temperature, the simulations yield values for the vapour density and temperature as well as for the particle flux which confirm the assumption of Hertz about an outgoing half-sided Maxwellian which implies alpha = 1. (b) For all temperatures, the density profiles do not change significantly in the liquid and in the interface in comparison with equilibrium. (c) For the medium and high temperatures, the kinetic temperatures somewhat decrease already in the liquid and more in the interface which leads to a lower particle flux than assumed by Hertz and hence alpha decreases with temperature. Finally, a simple correlation is given to estimate alpha as a function of T/T-c. (C) 2014 Elsevier Ltd. All rights reserved.