It is often desired to conveniently estimate the strength of materials by using specimens with small sizes. For this purpose, axial compression bending tests were examined by using carbon films and carbon fiber/epoxy resin unidirectional composite strands. The bending strength estimated from the axial displacement and the compression load coincided with the bending strength estimated from the deflection and the compression load. The carbon films showed specimen length dependence of the bending strength. The carbon fiber composite strand with a short specimen length produced a falling load compression curve. It was shown that the bending strength of the specimens showing falling load compression curves can be practically estimated by using the effective cross-section sizes at fracture. This analysis method is preferable also in order to minimize the error in the bending strength caused by the error in the cross-section size.