The mechanical behavior of heterogeneous carbonate rocks exhibiting total volumetric strain curves of type 2 was studied. Studied rock samples exhibiting a wide range of mechanical properties were collected from different geological settings of Israel. The results show that crack initiation for studied heterogeneous carbonate rocks occurs at significant standard deviations for all studied samples. Values of the difference (D) between the uniaxial compressive strength and crack initiation stress, and the ratio (k) between the crack initiation stress and uniaxial compressive strength are not constant even for samples within the same rock formation. The standard deviation of the mean k within the same rock formation varies between 0.03 and 0.12. Values of the maximum axial strain and maximum volumetric strain are 0.19/1.36% and 0.084/0.9%, respectively.