Abstract: Based on the experiments of creep fracture of rock-like cracks under compressive-shear load and biaxial compression, a subcritical propagation fracture toughness test on rock-like materials is made by using the constant displacement load relaxation method of double torsion specimens. The presence of creep fracture is confirmed on a laboratory-scale, and three creep fracture coalescence patterns are obtained: wing crack to wing crack, wing crack to primary crack, and wing crack to wing crack to shear crack. The creep fracture of rock-like materials is a stable crack growth essentially due to the subcritical propagation of rock-like cracks. Subcritical propagation occurs in rock-like cracks. Based on viscoelastic fracture mechanics, rheologic mechanics and energy principles, the corresponding potential functions are deduced in which inner variables are stress intensity factor, wing crack length and time. The creep fracture criterion and computational model for various damage effects and rock cracks under compressive-shear load are established. Using the experiments of creep fracture to verify these computational models, the theoretical time agrees with the experimental one of creep coalescence. The error between the experimental results and theoretical models will be larger when the propagation direction of wing crack is far away from the direction of the maximum pressure stress. The proposed method and theoretical criterion will provide a new and practical tool for studying the microscopic mechanism of creep fracture of rock cracks and the macro-mechanism of creep fracture in rock engineering.