This paper presents numerical modeling techniques to capture the behavior of the triple friction pendulum (TFP) isolation bearing when rotation is permitted about the horizontal axes of the top and bottom components. This paper builds on a previous model for the TFP bearing presented by the authors that is based on the kinematic and constitutive relationships of the individual components of the TFP bearing. The effect of rotation on cyclic bearing behavior and seismic system behavior are investigated numerically for two cases: constant support rotation and variable support rotation. It is found that constant support rotations should be limited in amplitude to ensure standard TFP bearing behavior. Results suggest that flexible supports may not have a large effect on global structure performance as long as typical deformation limits for the supporting members are met. In cases of both constant support rotations and flexible supports, the hardening stages of TFP bearing behavior are diminished. Copyright © 2013 John Wiley & Sons, Ltd.