Abstract Monte Carlo simulation is carried out for Lennard–Jones fluids for finding some of their basic physical properties under wide pressure and temperature changes. It is found from this simulation that for a given bulk fluid temperature the fluid mass density is linearly increased with the increase of fluid pressure, while for a given fluid pressure, the fluid mass density is linearly reduced with the increase of bulk fluid temperature. On the other hand, it is found that for a given fluid mass density the variation of fluid pressure is directly proportional to the variation of bulk fluid temperature. These findings support the corresponding results found and the statement made in the paper in Ref. [Y.B. Zhang, Industrial Lubrication and Tribology 58 (2006) 2], on which the theory of fluid shear strength is based.