A theoretical analysis model is presented to investigate the nonlinear dynamic behavior of bump-type foil bearings, i.e., the instability and unbalance response. In the developed model, the foil structure of bump-type foil bearings was simulated using the link-spring model, which was presented and validated in a previous study. During the calculation, the Reynolds equation and the foil structure model were coupled though the pressure and film thickness. An iteration solution method with the equation of shaft motion was applied for the shaft orbit. Parametric studies of design parameters, such as the bump number, the length ratio of the segment between two bumps and a bump, the foil thickness, the bump height, and the Young's Modulus, were presented upon the analysis of static performance and the instability of bump-type foil bearings. It is noted that more bumps or lager length ratio lead to larger load capacity. But the bearing load capacity does not change with different bump heights. Moreover, the threshold speed of instability decreases significantly with the rise of the bump number, especially when the number of bumps is low. However, it almost does not affect by other four parameters.