This paper proposes a new effective multiaxial plasticity model to simulate inelastic cyclic buckling in steel frame members. The proposed constitutive formulation is expressed within the framework of rate-independent metal plasticity and replicates the prepeak and postpeak responses of steel beam column members due to yielding and inelastic local buckling. Under compressive stress states in the postpeak regime, the constitutive formulation exhibits a softening behavior that is inferred from appropriate yield line mechanisms that idealize the onset and progression of inelastic local buckling of steel plates. The subsequent recovery of those buckling deformations under load reversals from the postbuckling regime is modeled using Bezier curves. An energy-based rule is formulated at the material scale to account for the observed in-cycle deterioration of the effective compressive stress at capping. The proposed constitutive formulation is general and can represent a broad range of softening and recovery phenomena. A regularization procedure was proposed for three-dimensional fiber-based beam column elements to mitigate mesh dependency in the presence of a softening material. The proposed formulation is implemented in a general-purpose three-dimensional nonlinear frame analysis simulation program. The ability of the proposed modeling approach to predict the response of steel beam columns subjected to cyclic loading histories is demonstrated by comparisons with available experiments and complementary continuum finite-element simulations in steel beam columns under cyclic loading that are susceptible to inelastic local buckling.