As kinds of unique textiles with high extensibility and elasticity, elastic fabrics are widely used for sportswear, medical textiles and electronic textiles. The tensile behavior of fabric is very important for post-processing and usage of fabric. However, there are very few studies on the resultant yarn strain subjected to the applied fabric extension, which is crucial for understanding the tensile behavior of elastic fabric and expanding its potential applications. In order to address the tensile behavior of elastic fabric, a mechanical model of fabric was built for the analysis of local yarn strain within the fabric through finite element method (FEM). The FEM models with full consideration of the tensile property of elastic yarns were built to predict the relationship between the applied fabric strain and the resultant yarn strain. An experimental study was conducted to characterize the yarn deformation behavior during the fabric stretching and compare with the FEM prediction. The FEM simulations show a good agreement with the experimental results. Based on the FEM models, the effects of fabric structural parameters on such a relationship were investigated for understanding the deformation mechanism and thus optimizing the tensile properties of fabrics. A yarn strain of 27.5% could be achieved under 60% fabric strain by adopting an optimized warp yarn spacing of 0.8 mm. The results not only shed light on the origin of high extensibility and elasticity of fabrics but are of great value to the design and development of elastic materials for various applications such as textile-based electronics.