To investigate relevance of the definition of the reference stress to estimate J and $C^{*}$ for surface crack problems, this paper compares FE J and $C^{*}$ results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface crack and finite internal axial crack are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) the local limit load, (ii) the global limit load, (iii) the global limit load determined from the FE limit analysis, and (iv) the optimized reference load. It is found that the reference stress based on the local limit load gives overall excessively conservative estimates of J and $^{*}$. Use of the global limit load clearly reduces the conservatism, compared to that of the local limit load, although it can provide sometimes non-conservative estimates of J and $^{*}$. The use of the FE global limit load gives overall non-conservative estimates of J and $^{*}$. The reference stress based on the optimised reference load gives overall accurate estimates of J and $^{*}$, compared to other definitions of the reference stress. Based on the present finding, general guidance on the choice of the reference stress for surface crack problems is given.