Considering the friction between bump foil and surrounding structure and the interaction between bumps in bump foil, the bending moment of the bump foil including a rounding between bump and bridge was established based on the elastic deformation energy theory. The foil deformation and stiffness of single bump was obtained and the validity of the proposed model was verified by comparing with previous foil models. The effects of the rounding radius on the structural stiffness of gas bearing and the anisotropy performance are studied by simulating gas film force distribution with triangular load distribution. The simulation results show that with the increase of the rounding radius the number of pinned-down bumps decreases in a step-like manner, and the stiffness of pinned-down bumps first increases and then decreases whereas the stiffness of the sliding bumps decreases. There is an optimal rounding radius at which the mean stiffness of the bump foil has a maximum value. With the increase of friction coefficient, the stiffness of foil arch presents a non-linear upward trend, which effectively reduces the anisotropy of structural stiffness. With the increase of rounding radius, the anisotropy of the stiffness of the structure increases, but the influence degree is not as severe as the friction coefficient. The results above can provide theoretical reference for structural design of gas foil bearing.