Annulus fibrosus (AF) injuries commonly lead to substantial deterioration of the intervertebral disc (IVD). While tissue engineering has recently evolved into a promising approach for AF regeneration, it remains challenging due to the cellular, biochemical, and mechanical heterogeneity of AF tissue. In this study, we explored the use of AF-derived stem cells (AFSCs) to achieve diversified differentiation of cells for AF tissue engineering. Since the differentiation of stem cells relies significantly on the elasticity of the substrate, we synthesized a series of biodegradable poly(ether carbonate urethane)urea (PECUU) materials whose elasticity approximated that of native AF tissue. When AFSCs were cultured on electrospun PECUU fibrous scaffolds, the gene expression of collagen-I in the cells increased with the elasticity of scaffold material, whereas the expression of collagen-II and aggrecan genes showed an opposite trend. At the protein level, the content of collagen-I gradually increased with substrate elasticity, while collagen-II and GAG contents decreased. In addition, the cell traction forces (CTFs) of AFSCs gradually decreased with scaffold elasticity. Such substrate elasticity-dependent changes of AFSCs were similar to the gradual transition in the genetic, biochemical, and biomechanical characteristics of cells from inner to outer regions of native AF tissue. Together, findings from this study indicate that AFSCs, depending on the substrate elasticity, have strong tendencies to differentiate into various types of AF-like cells, thereby providing a solid foundation for the tissue engineering applications of AFSCs. Statement of significanceRepairing the annulus fibrosus (AF) of intervertebral disc (IVD) is critical for the treatment of disc degeneration disease, but remains challenging due to the significant heterogeneity of AF tissue. Previously, we have identified rabbit AF-derived stem cells (AFSCs), which are AF tissue-specific and hold promise for AF regeneration. In this study, we synthesized a series of poly(ether carbonate urethane)ureas of various elasticity (or stiffness) and explored the potential of induced differentiation of AFSCs using electrospun PECUU scaffolds. This work has, for the first time, found that AFSCs are able to present different gene expression patterns simply as a result of the elasticity of scaffold material. Therefore, our findings will help supplement current knowledge of AF tissue regeneration and may benefit a diversified readership from scientific, engineering, and clinical settings whose work involves the biology and tissue engineering of IVD.