This work presents a mathematical model for the compressive strength of a rigid rod polymer fibre based on an approach describing the fibre fibril as an end-loaded column on an elastic base. Also, it is suggested that the model of elastic stability of the coated fibre includes the influence of thermal stresses. A good agreement with experimental data is received. From this model one can propose that if an interfibrilar matrix material is incorporated in the fibre, at a small volume fraction of about a few per cent, this material may have a pronounced influence on the fibre’s compressive strength.