Four known regularities; including the common bulk modulus, the common compression point, Tait–Murnaghan and the linear behavior of the P– T isochors; are investigated for the hard core one Yukawa (HCOY) and hard core double Yukawa (HCDY) fluids. It is shown that the HCOY fluid is not able to predict the common bulk modulus and the common compression points properly. While, these regularities are observable in the HCDY fluids and it can be shown that the common intersection point occurs where contribution of the repulsion terms to the equation of state is equal to that of attraction terms. The effect of hard core potential shape on these regularities is also investigated. The results show that the application of the hard convex core in HCDY equation of state just affect the common bulk modulus and common compression points slightly, but has no significant effect on other studied regularities.