The results are presented of an approximate elastic stability analysis for an anisotropic polymer fibre under compressive stress, which is embedded in an isotropic elastic matrix. This case, which thus far has not been treated properly, corresponds most closely to the experiments, which yield the best quantitative measurements of the compressive strength of high-modulus polymer fibres. Within the limits of a weak matrix, i.e. the shear modulus of the matrix is small compared to the shear modulus of the fibre, a simple analytical formula has been obtained for the compressive strength of the fibre in terms of its longitudinal Young’s modulus, and the Poisson’s ratio and shear modulus of the matrix. On the other hand, for a strong matrix the compressive strength of the fibre is solely determined by its shear modulus. For the intermediate regime, a simple but highly accurate interpolating expression has been constructed.