Pushover analyses are increasingly being used by the offshore industry in the assessment, and design, of offshore structures. Traditionally, such analyses are conducted on the basis that the tubular joints are assumed to be rigid. Whereas special finite elements for capturing the buckling behaviour of beam-columns have been in existence for some years, there has been no comparative approach for dealing with tubular joints, that is until the work reported in this paper. The work was carried out under the aegis of a major international Joint Industry Project concerned with the development, testing and calibration of an efficient analysis tool that allows the non-linear behaviour of tubular joints within a space frame structure to be appropriately accounted for. Pushover analysis incorporating proper joint behaviour can now be efficiently conducted with minimal user intervention. The paper describes the algorithms that were developed to simulate the non-linear behaviour of tubular joints under combined axial, in-plane and out-of-plane moment loads, across the full range of the load-deformation response. The (uncoupled) P-δ and M-θ responses were first represented by powerful, yet simple, equations whose coefficients were established by reference to test data. Coupling, for combined loads, was achieved by adapting plasticity theory algorithms. The interaction of chord loads on joint response and how the issue of joints having mixed K/X/Y classification is encompassed in the algorithms is addressed. Ductility limits and unloading behaviour are discussed. Finally, testing of the codified algorithms and calibration against frame test data are mentioned. The results demonstrate that frame response is more accurately captured when joint behaviour is taken into account.