The authors considered the energy condition of propagating crack based on the assumption that the surface energy absorbed at the tip of crack in newly created fracture surface is supplied from a circular region around the tip of crack. They represented the energy condition by eq. (11) and obtained the following conclusions; (1) In a completely continuous material the limiting constatnt velocity of crack is equal to that of Rayleigh wave. (2) In materials including no micro-cracks, the limiting constant velocity of crack propagation is nearly equal to and lower than that of Rayleigh wave. (3) In real materials with micro-cracks, the fracture propagates discontinuously and the limiting constant velocity falls down to the order of experimental value. The measured crack velocity will scatter beyond the range of the experimental error. (4) In low velocity state, the higher is the applied stress, the higher is the crack velocity. But, when the velocity of crack is nearly equal to that of Rayleigh wave, the applied stress affects little. (5) When both the applied stress and the elastic modulus are constant, the larger the specified surface energy is, the lower the crack velocity is. It has to be added that the discussion in this report is on the necessary condition for the crack propagation with a constant velocity and not on the necessary and sufficient condition for the brittle fracture propagation.