Buckling-restrained braces (BRBs) are often idealized with rate-independent simulation models. However, under dynamic loading, BRBs featuring low-yield point steel exhibit rate-dependency that may lead to appreciable amplifications of the BRB forces. This paper proposes a new rate dependent model for simulating a BRB's response under dynamic excitations. The proposed model consists of a displacement-dependent asymmetric Menegotto-Pinto material law and a velocity-dependent bilinear oil damper model. The calibration process of the proposed model is also presented. Two approaches are demonstrated in which the proposed model can be utilized within a nonlinear frame analysis program. A comparative study based on test data from full-scale shake table tests of a five-story steel building equipped with BRBs underscores that if their rate-dependency is neglected then the BRB local force demands may be significantly underestimated. This may also lead to erroneous predictions of lateral story drift demands as well as absolute floor accelerations during earthquake shaking.