Abstract: With axial internal surface cracked pipes under internal pressures as the research object, the creep fracture parameter C^* estimation method proposed by Zahoor was improved by introducing the x₀ parameter to make the J-integral full plastic solution independent of Norton indexes.The C^* values under the conditions of different Norton indexes and different crack size were calculated by the improved method, Zahoor solution, and reference stress methods including R6 global solution and Kim solution, and were compared with the finite element calculation.The results show that the C^* values calculated by the reference stress methods were two to eight times higher than those by the finite element calculation; the accuracy of the reference stress methods was poor.The ratios of the C^* values calculated by the improved method to the finite element calculation results were close to 1; the accuracy of the improved method was relatively high.Comparing with the Zahoor solution, the improved method had higher calculation accuracy with the Norton index of 3.But as the Norton index increased, the calculation accuracy of the two methods tended to be the same.