Summary: We present the results of non-equilibrium molecular dynamics simulations of planar shear flow and planar elongational flow of melts of model linear chain molecules, in which the number of beads per molecule is varied from \(N=4\) to 50. The shear viscosity \(\eta\), normal stress coefficients \(\varPsi_1\) and \(\varPsi_2\), and the two planar elongational viscosities \(\eta_1\) and \(\eta_2\) have been computed as a function of strain rate. The results are analysed using the third order retarded motion expansion (RME). The limiting zero strain rate values of the viscosity ratios agree with their expected values: \(\eta_1/\eta =4\) and \(\eta_2/\eta_1=0.5\). At low \(N\), values of the coefficient of the lowest order nonlinear term in the RME obtained independently from the shear flow simulations and the elongational flow simulations also agree. However, the consistency check fails for a higher order retarded motion coefficient. This is attributed to insufficient data at low strain rates for the higher values of \(N\). The \(N\)-dependence of the viscosities and normal stress coefficients as well as higher order RME constants is studied. We find that the zero strain rate values of the shear viscosity and both elongational viscosities are approximately proportional to \(N\) and the limiting values of the first and second normal stress coefficients \(\varPsi_1\) and \(\varPsi_2\) are approximately proportional to \(N^3\). The higher order RME constants have exponents nearer to 6.