Numerical modelling and design of cold-formed stainless steel members require accurate knowledge of the material stress-strain behavior over wide ranges of tensile and compressive strains. While many stress-strain models for stainless steels have been developed, when both tensile and compressive behaviors are considered, they are either only capable of accurate predictions over limited strain ranges or defined by rather complex mathematical expressions. This paper presents a new stress-strain model for stainless steel alloys. The proposed stress-strain model, while expressed using simple mathematical expressions, can accurately predict both tensile and compressive full-range stress-strain curves. The proposed stress-strain model is defined using the three basic Ramberg-Osgood parameters and based on a careful interpretation of a large experimental database covering wide ranges of strains. While the proposed stress-strain model is based on the staged approach similar to the existing stress-strain models, a novel method is used to define the second stage strain hardening exponent. Observing the fact that the strain hardening exponent tends to vary with the stress level, the second stage strain hardening exponent is defined in the proposed model as a function of stress level. For use in this model, the best existing equations for predicting the nominal ultimate stress and the corresponding strain (i.e., nominal ultimate strain) respectively are selected through an assessment of existing equations with experimental data. Comparisons between predictions from the proposed model and experimental stress-strain curves for three common structural classes of stainless steel alloys are presented. These comparisons demonstrate clearly the better accuracy of the proposed model over the existing full-range stress-strain models