The performance of gas foil bearings (GFBs) relies on a coupling between a thin gas film and an elastic structure with dissipative characteristics. Because of the mechanical complexity of the structure, the evaluation of its stiffness and damping is still largely inaccurate if not arbitrary. The goal of this paper is to improve the understanding of the behavior of the bump-type FB structure under static and dynamic loads. The structure was modeled with finite elements by using a commercial code. The code employed the large displacements theory and took into account the friction between the bumps and the support and between the bumps and the deformable top foil. Static simulations enabled the estimation of the static stiffness of each bump of a strip. These simulations evidence a lack of reliable analytical models that can be easily implemented in a FB prediction code. The models found in the literature tend to overestimate the foil flexibility because most of them do not consider the interactions between bumps that seem to be highly important. The transient simulations allowed the estimation of the dynamic stiffness and the damping of a single bump of the FB structure. The presence of stick slip in the structure is evidenced, and hysteretic plots are obtained. The energy dissipation due to Coulomb friction is quantified in function of materials, excitation amplitude, and frequency. Some energetic considerations allow the calculation of the equivalent viscous damping coefficient, and the results are related to experimental data found in literature. The influence of the number of bumps is also briefly addressed.