The paper introduces a simplified structural model for the numerical investigation of bump-type foil bearings. This analytical model is based on an efficient nonlinear contact procedure with consideration of friction, small deformations, and elasticity. The bump foil is modeled with a truss structure, while the top foil uses two-dimensional (2D) beam elements. In this present model, the normal and tangential contact forces between the bump foil and the bearing sleeve and between the foils are dealt with the penalty method. Even for a simple loading, the contact state might change between separation, stick, and slip. To avoid convergence problems caused by discontinuity, the regularized smooth friction model is used instead of the Coulomb friction model. In addition, due to contact problems that depend on time are accompanied by nonlinear evolution, the solution of the system equation using the incremental iterative method and the Newton–Raphson method is presented. The deflection of the top foil is added to the film controlled by the Reynolds equation (RE) to obtain the air pressure distribution. The theoretical predictions of the rotor push-pull tests agree well with results from the literature, which verifies the validity of the model. Using this present model, the quasi-static behaviors of the foil structure are mainly discussed, and parametric studies concerning environmental pressure and radial clearance are also conducted.