Rigorous analysis of polarization preserving optical fibres with three-layer elliptical cross-section is attempted, using Yasuura's mode-matching method with Bessel function expansion. The characteristics of the difference ΔBin the normalised propagation constants between two orthogonal dominant modes, which indicate the degree of polarisation-preservation, are investigated in detail for several combinations of the shapes of two boundaries, that is core-inner cladding and inner-outer claddings, with properly selected values of the refractive indices of the three regions in the cross-section. As a conclusion, better configurations for a polarisation-preserving single-mode fibre are discussed in detail for each three-layer dielectric optical fibre.