Comparison of different methods for the prediction of failure time and the determination of the safety limit for structure cracking in creep conditions is presented in this paper. Analyses using fracture mechanics (FM) and damage mechanics (DM) tools have been performed. In the case of FM, the C*-integral and C(t)-integral are used. For DM models, the Kachanov equation was chosen as the basic one. To avoid the strain and damage localisation and thus the mesh-dependence of the solution, the nonlocal integral method was used. The simulations of creep crack growth were presented for a compact tension sample made of 316 stainless steel at a temperature of 550°C. The problems encountered when solving the problem with the selected methods were listed. The results attained by analysed methods were compared and the most appropriate results were indicated. Obtaining a satisfactory solution of the given problem is difficult. Presented methods allow to achieve some approximations of the time to failure in relatively simple manner. They can be especially useful when not the absolute but relative solutions, like safety factors, are seek.