In this paper, the non-probabilistic failure assessment method for a pipe with crack was proposed, and interval model was applied in this assessment method. Compared with the deterministic approach, the assessment parameters were regarded as interval parameters in the non-probabilistic method, which could reflect the uncertainty of data and avoid the unsafety of results caused by the scatter of these parameters. On the other hand, compared with traditional probabilistic method, the non-probabilistic method only needs the range or bound of the parameters rather than detailed statistics information of the parameters which may be uneasy to be obtained from practical engineering. So the new assessment method reduces the request for detailed statistics properties of parameters. In this paper, load, material mechanical properties and the size of crack were treated as interval parameters, and the non-probabilistic failure assessment method was established based on the level 2 normal assessment of the BS 7910:2005. In this case, the assessment point (Lr, Kr) is not a deterministic value, Lr and Kr would vary in a certain interval. As a consequence, the assessment point was changed into a rectangle zone, and the non-probabilistic failure measure for pipe with crack could be obtained by the variation of the rectangle. The non-probabilistic failure measure can be defined as the ratio of the area of failure region to the total area of the rectangle. At last, the non-probabilistic failure assessment method was used to evaluate a titanium pipe, and the analysis results were compared with the results of deterministic method, probabilistic method according to Monte-Carlo and partial safety factors method, respectively. The analysis results sufficiently demonstrated that the new non-probabilistic failure assessment method proposed in this paper was feasible and available.