Abstract Modelling the superplastic process using finite element analysis can enable optimum process parameters to be determined and lead to a better understanding of the process. Constitutive equations, which accurately represent a material’s behaviour, are very important in the development of representative process models. The development of a set of constitutive equations for superplastic grade Inconel 718 alloy based around a hyperbolic sine relation is described in this paper. The hyperbolic sine relation with strain dependant parameters is shown to represent the relationship between stress, strain and strain rate over a wide strain range. The valid strain range is sufficient to cover both strain hardening and flow softening behaviour.