Buckling-restrained braces (BRBs) permit exploiting the hysteretic properties of their core material both in tension and compression. However, the global behaviour of BRBs does not fully replicate the local behaviour of their core material and require the use of specific constitutive models. An elastoplastic model for steel BRBs allowing a straightforward physical interpretation of the constitutive parameters of the model, explicit computation of response quantities related to failure and dissipated energy, showing good predictions of the experimental behaviour, is implemented into OpenSees. The implemented algorithms include response and consistent response sensitivity results to the BRB material and geometric parameters. Specifically, response sensitivity results are obtained through the direct differentiation method (DDM) and validated through the forward finite difference method (FDM). Selected results for response and response sensitivity analysis are illustrated and discussed using as a case study a realistic multi-storey steel frame with BRBs subjected to a selected set of seismic accelerations. The presented response sensitivity results can be used to gain further insight into the influence of the BRB behaviour on the global and local structural response as well as a basis for the use of gradient-based methods as for example adopted in structural optimization and model updating.