Mechanical damage on tensile strength of carbon filament is tested by three methods with PAN- and pitch-based fibers. No effect on tensile strength by keeping pre-tension at the level of mean tensile fracture load is made sure. By prior transverse compressive loading on cross-piled up filaments, many filaments are crushed by a small load. Tensile strength of the survival filament has no influence on a PAN-based carbon fiber, but has decreased in case of a pitch-based carbon fiber. Two steps torsional-tensile test is carried out, that is, first step is keeping pre-tension to the mean tensile fracture stress at a rotation, and second step is the survival filament is tested by tension without rotation, or the opposite way of testing, the first step is at simple tension until the mean strength, and the second step is estimation the torsional-tensile strength with a shear stress by a rotation. It is found the tensile strength and the torsional-tensile strength have related each other for a PAN-based fiber until the torsional fracture strain, however the torsional-tensile strength of a pitch-based carbon fiber become no relation at higher torsional strain with the tensile strength. Those differences between PAN- and pitch-based carbon fibers are an influence from difference in degree of strength anisotropy in macroscopic viewpoint, and derived from the structural differences in cross section in microscopic viewpoint.