Step-by-step (SBS) stair navigation is used by those with movement limitations or lower-limb prosthetics and by humanoid robots. Knowledge of biomechanical parameters for SBS gait, however, is limited. Inverted pendulum (IP) models used to assess dynamic stability have not been applied to SBS gait. This study examined the ability of the linear inverted pendulum (LIP) model and a closed-form, variable-height inverted pendulum (VHIP) model to predict capture-point (CP) stability in healthy adults executing a single stair climb. A second goal was to provide baseline kinematic and kinetic data for SBS gait. Twenty young adults executed a single step onto stairs of two heights, while attached marker positions and ground reaction forces were recorded. opensim software determined body kinematics and joint kinetics. Trials were analyzed with LIP and VHIP models, and the predicted CP compared to the actual center-of-pressure (CoP) on the stair. Lower-limb joint moments were larger than those reported for step-over-step (SOS) stair gait. Leading knee rather than trailing ankle was dominant. Center-of-mass (CoM) velocity peaked at push-off. The VHIP model accounted for only slightly more than half of the forward progression of the vertical projection of the CoM and was not better than LIP predictions. This suggests that IP models are limited in modeling SBS gait, likely due to large hip and knee moments. The results from this study may also provide target values and strategies to aid design of lower-limb prostheses and powered exoskeletons.