Attempts were made to estimate the fibre axial compressive strength of pitch-based graphitized and polyarylate fibres, and the relationship between the compressive strength and fibre diameter was investigated. The estimated compressive strength of fibres decreases with increasing temperature. This decrease in compressive strength may be accounted for by a decrease in the radial compressing force. There is a linear relationship between the estimated compressive strength and radial compressing force in a temperature range from room temperature to 80°C. The real compressive strength of the fibres, determined by extrapolating this straight line until the radial compressing force is zero, increases with decreasing fibre diameter, but remains almost unchanged at a diameter range smaller than 10 μm. In order to obtain reinforcing fibres having a higher compressive strength, it will be necessary to prepare fibres having a diameter smaller than 10 μm.