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The thermoelastic response of thin gold films induced by femtosecond laser irradiation is numerically simulated using a modified combined two-temperature model (TTM) and molecular dynamics (MD) method, with focus placed upon the influence of the electron relaxation effect. The validity of the numerical approach is checked against existing experimental results. While the electron relaxation effect is found negligible when the laser duration is much longer than the electron thermal relaxation time, it becomes significant if the laser duration matches the electron relaxation time, especially when the former is much shorter than the latter. The characteristics of thermo-mechanical interaction in the thin film are analyzed, and the influence of temperature-dependent material properties upon the thermoelastic response of the film quantified.