A series of fracture toughness tests have been conducted on a type of coarse grain marble. The tests were carried out either in pure mode I or in pure mode II conditions by using the cracked chevron notched Brazilian disc (CCNBD) specimen. A total number of 44 CCNBD specimens were tested, half in pure mode I and the rest in pure mode II, to obtain reliable values for mode I and mode II fracture toughness (KIc and KIIc) of the tested marble. The average value of KIc for this marble was approximately about 1.12 MPa m showing a good agreement with those reported for similar coarse grain marbles. The mode II fracture toughness was found to be 2.25 MPa m in average which is approximately twice the mode I fracture toughness. However, the conventional fracture criteria suggest that the mode I fracture toughness should be higher than the mode II fracture toughness, (KIc>KIIc). According to these criteria, the ratio of KIIc / KIc is a figure typically between 0.63 and 0.96. It is shown in this paper that enhanced mode II fracture toughness of CCNBD specimen could be due to the effects of highly negative T-stress when the specimen is subjected to mode II. It is also shown that an improved prediction for the ratio KIIc / KIc can be achieved when the effect of T-stress is taken into account.