The use of buckling restrained braces (BRBs) is gaining popularity both for new construction and rehabilitation projects in seismic areas. As buckling is prevented, the core of the BRB can develop axial yielding in compression in addition to axial yielding in tension, permitting an hysteretic behaviour of the BRB similar to that of the material of the core. As a result, BRBs with steel core could be modelled using cyclic models already available and commonly used in the literature for structural steel. However, available models do not address completely some highly desired requirements: appropriate isotropic hardening that has an important role in BRB behaviour, non symmetric tension-compression response as observed experimentally, explicit computation of the plastic component of the deformation as required in BRB capacity models, smoothness of the elastic-plastic transition, simple implementation and limited number of input data parameters to facilitate its implementation and use. Therefore, a cyclic elastoplastic model for steel BRBs is presented following a simple and consistent approach based on a rheological scheme that requires the use of only one internal variable. The formulation adopted allows a straightforward interpretation and identification of the constitutive properties of the model as well as the explicit computation of response quantities related to failure and dissipated energy. Specific BRB behavioural aspects are addresses with an appropriate isotropic hardening rule as well as non symmetric tension-compression response. Response results obtained using the proposed model are discussed and compared to various experimental test results available in the literature, showing an easy identification of the constitutive parameters required and accurate predictions of the BRBs experimental response.