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A new computer geometric modeling approach for 2 × 1 and 3 × 1 twill woven fabric structures is proposed. The precise geometrical description is presented by taking the skewness property into account. In the 2 × 1 and 3 × 1 twill weaves, the twill fabrics are formed of asymmetric floatings in which the length of floating sections was not equal on both surfaces and therefore the equilibrium condition was different from symmetric floatings. The proposed algorithm has three main parts: the first part describes the two-dimensional model of yarn cross-section for twill woven fabric structure, the second part consists of a modeling method for a three-dimensional model in warp/weft yarn, and the third part contains the CAD model. Examples of this approach are demonstrated and compared with a single line of yarn path model and the filament assemble model that excludes the skewness property. The model simulated in this study can improve the visual simulation of the real twill woven fabric and also this geometric model necessary as an input to many computational models for the prediction of the properties of the fabrics. [ABSTRACT FROM AUTHOR]