This paper introduces a time-efficient reduced model for gas foil bearings. The foil structure of the considered air foil bearing can be modeled very realistically by a quasistatic nonlinear stiffness/friction hysteresis model; the gas film is assumed to be stiff enough to be neglected for the nonlinear forced response analysis. The main objective is to carry out nonlinear simulations of rotors with foil bearings in time domain. An important feature of the model is to enable fast run-up simulations, while maintaining important physical properties of the bearing. Furthermore, the determination of the model parameters should be simple to enable a fast adaption of new foil bearing geometries into existing rotor models. Finally, it should be possible to implement the bearing model very easily into arbitrary rotordynamic or multibody software tools. The basis of the approach is a two-dimensional hysteresis model, which approximates the nonlinear relationship between the movement of the rotor journal and the corresponding bearing forces. Although the here presented reduced bearing model cannot predict instability effects generated by the air film, the model may capture the nonlinear behavior of the foil bearing accurately. Hence, the nonlinear response of the rotor-bearing system may be predicted very precisely, if the rotor speed is below the threshold speed of instability. The input data for the reduced bearing model are measured or simulated hysteresis curves. The relevant parameters that influence the accuracy and the limits of the numerical model are discussed. Different simulations with very detailed finite element bearing models are presented in order to demonstrate the accuracy of the reduced modeling approach.