For rock materials, a transversely isotropic failure criterion established through the extended Lade-Duncan failure criterion incorporating an anisotropic state scalar parameter, which is a joint invariant of deviatoric microstructure fabric tensor and normalized deviatoric stress tensor, is verified with the results of triaxial compressive data on Tournemire shale. For torsional shear mode with $0{leq}b{leq}0.75$, rock shear strengths decrease with ${alpha}$ increasing until the rock shear strength approaches minimum value at ${alpha}{approx}40^{circ}$, and after this point, the rock shear strengths increase as ${alpha}$ increases further. For the torsional shear mode with b > 0.75, rock shear strengths are almost constant for ${alpha}{leq}40^{circ}$, but it increases with increase in ${alpha}$ afterwards. The rock shear strength variation against ${alpha}$ agrees with shear strength changing tendency of heavily OCR natural London Clays tested before. Prediction results show that the transversely isotropic failure criterion proposed in the paper is reasonable.