This paper presents a study on the criterion of crack initiation and propagation under creep conditions, which were investigated using specimens collected from outcropped sandstone rock formations. Beam specimens under three points bending were used in this investigation. The experimental result shows that due to creep deformation, rock crack will inevitably initiate and propagate after a time interval of sustained loading under a load of KI, which is less than fracture toughness KIC but not less than a constant marked as KIC2. KIC2 indicates the ability of rock to resist crack initiation and propagation under creep conditions and it is defined as creep fracture toughness.