Advanced numerical modeling of cold-formed stainless steel members, from manufacturing to the full-range response under applied loading, requires knowledge of the stress-strain relationship of the material over a wide range of tensile and compressive strains. Although a number of stress-strain models have been developed for stainless steels, most of them are only capable of accurate predictions either over a limited range or for the tensile stress-strain behaviour only. Only two approaches by Rasmussen (2003) and Quach et al. (2008), respectively, can provide accurate predictions for stainless steels over the full range of strains up to the ultimate strain u  by using only the three basic Ramberg-Osgood parameters (0.2% proof stress  0.2 , initial elastic modulus E0 and strain-hardening exponent n ) as input data. These two existing models are regarded as the two-stage model (Rasmussen 2003) and the three-stage model (Quach et al. 2008) respectively. However, these two models were developed based on an interpretation of limited available experimental data from virgin materials and flat materials (flat portions of cold-formed sections) of austenitic, ferritic and duplex alloys. Hence, these two models are not applicable to corner materials and materials with a greater amount of cold work, and they are also not applicable to lean duplex alloys and high strength austenitic alloys (H.S.A.) which become more popular in structural applications. This thesis is concerned with two new full-range stress-strain models for stainless steels which are capable of accurate predictions over the full range of strains up to the ultimate strain. These two proposed models are applicable to a wide range of stainless steel alloys (including austenitic, ferritic, duplex, lean duplex and H.S.A. alloys) with different levels of cold work (i.e., no cold work, intermediate and high ii cold work). Hence, the two proposed models can overcome the shortcomings of the existing models proposed by Rasmussen (2003) and Quach et al. (2008). These two new stress-strain models are expressed in terms of the three basic Ramberg-Osgood parameters and some additional parameters. Empirical expressions for these additional parameters have also been developed based on a careful interpretation of existing experimental data from different parts and types of cold-formed stainless sections with various levels of cold work and a wide range of stainless steel alloys. Thus, the proposed models can be finally defined using the three basic Ramberg-Osgood parameters only. The accuracy of the proposed models has been demonstrated by comparing their predictions with experimental results. The advantages of the proposed models have also been demonstrated through the comparison of their predictions with predictions from existing models.