Bearing capacity of foundation is conventionally calculated based on the linear Mohr–Coulomb failure criterion. However, a amount of experimental data shows that the strength envelops of almost all types of rocks are nonlinear over the wide range of normal stresses. The strength envelope of rock masses is considered to follow a modified Hoek Brown nonlinear failure criterion. Therefore, according to the upper bound approach, based on Hoek Brown nonlinear failure criterion and a multi tangential technique method, the relevant programs were developed by means of the software Matlab and the sequential quadratic programming optimization theory. And the calculation and the analysis of affecting factors bearing capacity for rock foundation were employed. It is found that the major factors affecting bearing capacity of rock foundation are GSI and mi, but the weight of foundation ,overload and the disturbance coefficient of excavation D have a considerable influence on bearing capacity of rock foundation when the value of GSI is small . Compared with the generalized tangential and the finite element or finite difference numerical techniques, the single tangential technique method would bring relatively great risk, because the calculation results are larger than those of the actual bearing capacity of foundation.