In this paper, rotational spring and multi-spring models are implemented in SAP2000® software, and numerical solutions are presented for monotonic and cyclic behaviour of a dissipative controlled rocking (DCR) bridge column supported on a monopile foundation that is embedded in sand. The pile-soil system is modelled with elastic frame elements connected to vertically-spaced bi-linear soil springs. Three soil conditions (i.e. loose, medium-dense and dense sand) are considered to account for soil-structure interaction effects. The results from an experimental programme, carried out by the authors at the University of Canterbury, are used to validate the numerical solutions. The numerical simulation results for the three sand conditions are in good agreement with the experimental ones. From a computational standpoint, the relatively simple mathematical formulation and easy implementation would make the rotational spring model more desirable than the complex multi-spring model. On the other hand, the multi-spring model is more versatile and capable of describing the cyclic response of the DCR pier, such as the post-tensioning force, axial stress in the steel dissipaters and gap-opening interface rocking characteristics.