The mechanical and damage properties of single fibres used in fibrous composite have gained tremendous importance in recent years. These properties are used in determination of effective properties of composites by micromechanics. These are also used in the micromechanical damage modeling. Further, these properties are used as an indicator of the excellence of product by manufacturers. In the present study the axial tensile modulus, ultimate strength and failure strain of single fibres are determined for carbon and glass fibres. ASTM D3379-75 standard is followed and a number of fibers are tested for statistical analysis. The axial tensile moduli measured are 246.7 GPa and 93.3 GPa, respectively and strength are 3031.6 MPa and 2035.9 MPa, respectively for carbon and glass fibres. Further, the respective axial tensile failure strains are 0.0137 and 0.0224. The error in the measurement of axial modulus is below 8% while for axial tensile strength is below 1%.