An efficient formulation for the response and dissipated energy of Bouc–Wen hysteretic model is proposed. The displacement is associated with the hysteretic parameter in terms of Gauss’ hypergeometric function. The hysteretic equation is solved analytically for specific values of the exponential parameter that controls the transition between elastic and inelastic regime. This formulation is used to provide analytical expressions of the dissipated energy under symmetric cyclic excitation, based solely on the model parameters and the displacement amplitude. For arbitrary values of the exponential parameter, the equations are solved numerically. For fully yielding systems, approximate relations are determined using suitable curve fitting. The derived expressions facilitate considerably the preliminary design of hysteretic systems.