Abstract Molecular dynamics (MD) employing the Lennard-Jones (LJ) interaction potential was used to compute the heat capacities of argon at constant volume \CV\ and constant pressure \CP\ near the critical point very close to the asymptotic region. The accurate \MD\ calculation of critical divergences was shown to be related to a careful choice of the cutoff radius rc and the inclusion of long-range corrections in the \LJ\ potential. The computed \CP\ and \CV\ values have very good agreement as compared to available \NIST\ data. Furthermore, values of \CV\ in a range of temperatures for which \NIST\ data is not available could be computed. In the investigated range of temperatures, both \CP\ and \CV\ \MD\ results were fitted to a simple mathematical expression based on an empirical model that describes the critical effects when the asymptotic models are not appropriate. The present approach is of general applicability and robust to compute thermophysical properties of fluids in the near-critical region.