摘要：In order to give a true reflection of the spatial structure of woven fabric, a circular mathematical model is established based on the Peirce's model and the principle of the coordinate transformation. The circular model uses arcs and tangent lines as the yarn flexion shape and selects the circle as the yarn cross-section. Then, a new elliptical cross-section mathematical model is rapidly built by the Jacobian transformation of the circular model. The Matlab software is used for the 3D simulation. It is shown that 3D simulations of woven fabrics with different weft and warp yarn counts, weft and warp densities, structure phases, weaves and flattening coefficients are successfully realized by Matlab basing on the elliptical mathematical model.