We present two numerical approaches to calculate the geometrical birefringence from two-dimensional refractiveindex profile in single-mode fibres. One is the improved perturbation model theory, the other is based on the general solution of noncircular uniform optical waveguide in an arbitrary coordinate system. Using these methods, we can obtain not only the magnitude of geometrical birefringence, but also the orientation of birefringent axes. We report the calculation results of geometrical birefringence in a real single-mode fibre.