An existing cyclic plasticity constitutive model is enhanced to simulate low-cycle fatigue and ratcheting responses of 304 stainless steel (SS) under proportional and various nonproportional loading cycles. Nonproportional loading and multiaxial ratcheting parameters, and strain range dependent cyclic hardening/softening modeling features are incorporated into a modified Ohno–Wang model to enhance its uniaxial and multiaxial loading responses. The improved constitutive model is incorporated in the commercial Finite Element Code ABAQUS through its user defined subroutine UMAT and the responses of 304 SS tubular specimen from literature have been simulated. The proposed model has demonstrated good correlation with uniaxial and different types of multiaxial fatigue and ratcheting responses. Two types of multiaxial loading cycles are studied; the first included axial and torsion cycles along different loading paths, and the second included steady internal pressure and axial strain or stress cycles. The axial–torsional loading cycles demonstrated axial and/or shear strain ratcheting, whereas the internal pressure-axial cycles demonstrated axial and/or circumferential strain ratcheting. Complex interactions between ratcheting strains in different directions along with the rate of ratcheting are simulated well by the improved Ohno–Wang model.