We present a novel method for performing steady state nonequilibrium molecular dynamics simulation of planar elongation flow based on the studies of Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)]. These authors identified the orientation of the unit cell which leads to periodic behavior of the square lattice with the minimum period. This way the exponential deformation of the system periodically returns to a state where replacing some of the original particles with their images the initial state boundaries are recovered. We adopted their theoretical results to nonequilibrium molecular dynamics simulations and performed representative calculations for simple fluids. The new method solves the long-standing problem of simulating planar elongation flow in the steady state.