This paper considers a new computer model of the mechanical behaviour of plain-knitted structures in uniaxial extension. The knitted structure is considered as a system of unit cells. The model of the mechanical behaviour of the unit cell takes into account the fabric structure, the mechanical behaviour of individual threads, and interaction between the unit cells. The computational results are in a very good agreement with the experimental data. This model can be extended to different knitted structures and to the prediction of 3D deformation. This paper advances theoretical and practical studies of textile mechanics in application to technical textiles.