Intralaminar fracture toughness of a fibre-reinforced angle ply and cross ply laminates are generally obtained by testing compact tension specimen and theoretically predicted using the well-known MCCI approach. The crack initiation direction, which is treated as a branch direction for the theoretical prediction, is an apriori. A conservative estimation on the toughness value obtained by considering branch crack angle corresponding to each fibre orientation in a laminate shows a gross error with respect to test data. In the present study a new criterion for the prediction of crack initiation angle is arrived at based on Tsai-Hill minimum strain energy density criterion. This shows a very good agreement with test data available in literature on fracture toughness of various multilayered composites with large size cracks with a/w ³ 0.3. It is interesting to note that in a multilayered composite a simple method of prediction in which crack initiation direction is assumed to be the fibre orientation that is close to the initial crack direction gives a good estimation of the intralaminar fracture toughness.