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Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding KIc and KIIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of KIIIc/KIc obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio KIIIc/KIc. Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.