Abstract: The transverse compression properties and failure features of glass fibre,carbon fibre and carbon/glass hybrid fibres composites are investigated with two epoxy resins as matrix.The fact that the experimental values of the transverse compression strength of composites are more than the theoretical values predicted by Greszczuk's formula, and Tsars formula and Chamis' formula are examined.The resul is are as follows 1.The transverse compression properties of composites rely on the properties of matrix and fibre.The transverse compression modulus is increased with matrix modulus.For the same matrix, the moduli are:GFRP>HFRP>CFRP. 2.The internal stress changement in composites under compression is different from that under tensile.Although the transverse compression strength of composites is mainly dependent on that of matrix,it is not less than but more than the compression strength of matrix.The prediction of the transverse compression strength can not imitate the treating method of the transverse tensile.3.The semi-emprical formula of the prediction for the transverse compression strength of composites is given.The predictions are in agreement with the experimental values and the formula is identified with the pretro-spective experiment.