In the current study multi-layered thick-walled fibre reinforced composite pipes under torsion loading are considered. To analyse the stress-strain distribution in the pipe the Finite Element model (ABAQUS) has been developed. Using the model the radial, hoop, axial and shear stresses have been calculated for different lay-ups of the fibre reinforced pipes, and modified Tsai-Hill failure coefficients have been computed. The validation of the model was done by comparing the results available in the literature and the semi-analytical three-dimensional elasticity solution. The dependence of the failure coefficient on winding angles and layers’ thickness was investigated and analyzed, and the appropriate design considerations have been suggested for four-layer pipes.