This paper proposes a new model for simulating the inelastic behavior of steel beam-columns exhibiting softening. A novel rate-independent multiaxial metal plasticity model is formulated to mimic nonlinear geometric effects (local buckling) through material softening. The governing equations that define the yield surface are presented. The evolution rules of the model at various loading paths are established. Asymmetric responses between tensile and compressive loading are explicitly considered. Prior to inelastic local buckling, the constitutive model follows J2 plasticity, with combined isotropic and kinematic hardening rules regardless of the loading conditions. Under compressive stresses, the constitutive model simulates the plastic buckling response of steel plates based on yield line mechanisms. The plastic mechanisms and the plate boundary conditions depend on the employed cross section. While the proposed approach is general, this paper focuses on steel beam-columns with hollow structural steel (HSS) profiles. With respect to inelastic cyclic buckling, a third order Bezier function is featured to idealize the recovery path of the post-buckling deformations. Cyclic degradation is accounted for by using a well-established energy-based rule, which is applied at the material scale. The developed multiaxial constitutive law is versatile and can be easily adapted to model a broad range of softening responses. The multiaxial material model is used in a 3-dimensional force-based beam-column element. The validity of the developed model is examined via comparisons with experiments and continuum finite element simulations on steel columns with HSS cross sections.