The behavior of composites made from carbon fibers and carbon matrix under loading on the transverse flexure and under loading on a shear has been investigated. The effect of the ratio of the length of the span to the thickness of the sample on the values of maximum stress at fracture of composites tested in transverse bending has been estimated. The limits to the values of this parameter for which its change does not affect the determined values of maximum stress at fracture of composites have been set. It is shown that the standards developed for the determination of transverse bending ultimate strength of composites with polymeric matrix, not all are suitable for carbon-carbon composites. A brief analysis of methods for determining the shear ultimate strength of composites with polymeric matrix has been made. The reasons for restricting their use for carbon-carbon composites have been noted. The methods of test for shear carbon-carbon composites, allowing obtaining the failure due to the shear in the estimated cross-section of samples have been proposed. The values of shear ultimate strength are not affected by the size of the samples in the range studied. The pattern of the stress distribution over the cross section of the sample in the case of shear testing prismatic specimens has been investigated