The use of jointed precast concrete and steel connections with unbonded, post-tensioned prestress has been the focus of a significant amount of recent research. These systems provide a controlled inelastic response through gap-opening at the beam-column interface instead of through yielding and damage of the structural elements. The development of a model that captures all of the associated characteristics and provides an accurate prediction of connection response provides significant added confidence in response simulations. A model is developed that utilises a time-incremental model of the connection behaviour that accounts for yielding of the prestress tendons, the reduction or elimination of the prestressing force, friction between the post-tensioning tendons and the containing ducts, and asymmetry from non-centrally located tendons. The model is formulated using incremental versions of the Menegotto-Pinto and Ramberg-Osgood type, providing a smooth, continuous loading and unloading approximation to the piecewise linear behaviour. The model is validated against experimental results for an 80% full-scale jointed precast concrete connection tested with inputs drifts to a maximum of 4%. Results show very good agreement between the model and the experimental results, with errors generally less than ±5%. Overall, the model is generalisable to other connections using steel and concrete rocking connections that utilise this damage-free design approach and is a useful tool for evaluation of connection designs.