Generally, rock strength criteria are obtained by the triaxial compression tests at the low confining pressure. However, the strength in these criteria tends to be higher than experimental data at the high confining pressure. To overcome this deviation, we propose a concept of rock critical state confining pressure. It can be deduced that deviator stress is constant and critical rupture angle is 45 degrees at critical state using this concept. It is then introduced to modify Mohr-Coulomb and Hoek-Brown strength criteria. The accuracy and applicability of these two modified criteria are verified by a series of triaxial experimental tests. It is noted that the parameters in modified criteria have lower sensitivity to the confining pressure than those in the original criteria. The modified criteria can not only maintain the consistency and accuracy in strength assessment at the low confining pressure, but also assess the consistency of experimental strength at high confining pressure. Thus, the modified criteria can be used to accurately estimate the strength of rock at the high confining pressure.