Carbon fibre-reinforced polymer (CFRP) and glass fibre-reinforced polymer (GFRP) woven composites are widely used in aerospace, automotive and construction components and structures thanks to their lower production costs, higher delamination and impact strengths. They can also be used in various products in sports industry. These products are exposed to different in-service conditions such as large tensile and bending deformations. Composite materials, especially ±45° symmetric laminates subjected to tensile loads, exhibit significant material as well as geometric non-linearity before damage initiation, particularly with respect to shear deformations. Such a nonlinear response needs adequate means of analysis and investigation, the major tools being experimental tests and numerical simulations. This research deals with modelling the nonlinear deformation behaviour of CFRP and GFRP woven laminates subjected to in-plane tensile loads. The mechanical behaviour of woven laminates is modelled using nonlinear elasto-plastic as well as material models for fabrics in commercial finite-element code Abaqus. A series of tensile tests is carried out to obtain an in-plane full-field strain response of [+45/-45]_2s CFRP and GFRP laminates using digital image correlation technique according to ASTM D3518/D3518M-94. The obtained results of simulations are in good agreement with experimental data.