The interlaminar shear strength and the flexural strength are usually determined by means of the three-points flexural test because of its simplicity. These strengths are defined as the maximum stress values predicted by elementary beam theory based on Euler-Bernoulli hypotheses. However, in the three-points flexural test on composite materials, especially with high anisotropy, the stress distribution in the vicinity of central loading point is not so simple as that given by the elementary beam theory. In the present paper, the multi-axial stress distributions in the three-points flexural test and the influences of various factors such as span/depth ratio and shape of load distribution on beam are analysed in order to discuss the validity of these fracture strengths and to propose a reasonable testing method. Consequently, it is found that the local stresses at the maximum bending moment region are very high, and that, in the case of small span/depth ratio, the stress distribution differs extremely from that based on the elementary beam theory. The validity of these analytical results is confirmed by using the finite element method analysis. The initial failure behaviors can be explained by these analytical results.