This paper illustrates some preliminary experimental, numerical and theoretical analysis results of mixed mode I-III rock cracks under apparent mode III loading. Some edge notched granite specimens are tested under out-of-plane four-points shearing loading condition, i.e., an apparent mode III loading condition. A series finite element analysis was conducted to understand the mechanism of the crack fracture propagation under this loading condition. The stress intensity factor distributions along the 3-D crack tips are also obtained. All crack fracture propagation surfaces of the specimens are similar helicoids which radius can be mainly influenced by the loading patterns, i.e., the action width s. The crack fracture initiates at the midpoint of the crack front. From the numerical calculation and experimental investigation, it has been revealed that all of these crack fracture initiations are caused by maxima tensile stress σ1. Based on this stress σ1, a new fracture criterion of mixed mode I-III is proposed. Its predictions agree well with the experiment results. This criterion can be applied to practice engineering designs which are related with mixed mode I-III or pure mode III rock crack fracture problems.