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In this study the tensile recoil test – an experimental technique to find the axial compressive strength of single fibres is discussed and the axial compressive strength of single carbon fibres has been determined for a fixed gauge length. Several fibres were tested at different stress levels and the data obtained regarding the failure of the fibre due to initiation of recoil compressive stress was used to determine the strength in compression. The recoil test data was evaluated using usual statistical and probabilistic models. Probabilistic Weibull and logistic models were used to evaluate the compressive strength distribution obtained from the recoil test. The axial compressive strengths of single carbon fibre predicted by all models are in good agreement with each other and the probabilistic models are very close to each other. The compressive strength of carbon fibres, is calculated as 869 MPa, which is very close to the value reported in the literature obtained by this method.