The soil under foundation is assumed to be a rigid plastic medium and obey Mohr–Coulomb failure criterion; slip-line theory has been used to determine the bearing capacity of rough strip footings. The bearing capacity of footings is calculated with the finite difference method for given boundary conditions. The value of bearing capacity factor Nγ is consequently obtained without superposition approximation. The formula shows that Nγ is not only related to internal friction angle of soil φ but also to the dimensionless ratio F. The Nγ is a constant with the determined φ and F. The calculated Nγ is compared with other researchers’ results. It’s found that different assumptions made by other researchers are chief factors that lead to errors. The calculations of Nγ with different values of F and φ are presented and compared with results. Finally

two forms of suggested expressions to approximate Nγ are proposed according to numerical calculations. The errors between approximated values and numerical results are clarified. The approximated results are close to the numerical ones so as to prove to be practical to evaluate the ultimate bearing capacity.