In the deep water S-lay installation, the buckle arrestor rolls on and drops off the rollers repeatedly when it moves along the stinger. When the buckle arrestor is located on the roller, there is strain intensification at the 12 o'clock position of the pipe section which is close to the buckle arrestor, and the strain can reach 1%. When the buckle arrestor drops off the roller, the strain decreases. The maximum strain occurs around the position where the girth welding is located, a defective girth welding part may fail under this cyclic loading. If an initial flaw exists, it is important to be able to predict the total crack growth under the cyclic loading process. The thesis is conducted in three stages. In the first stage, the global FE model is used to model the buckle arrestor behavior during its passage over the stinger, especially the bending moment variation. In the second stage, the output from the global model is used as input for the local FE model, to obtain the stress and strain of the pipe cross section. In the third stage, based on the local FEM output, Engineering Critical Assessment is carried out on the girth welding part, and the girth welding safety is judged by comparing the predicted crack growth with the limit standard. It is found out that the buckle arrestor is safe under realistic cyclic loading conditions. This is due to the relatively small strain range which cause little influence on the fracture resistance. The total crack growth can be treated as superposition of tearing growth and fatigue growth. In further extension, when the large cyclic strain range is applied, according to some experiments and numerical results, the simplified superposition method is not suitable. The compressive loading could reduce the crack tip fracture resistance. In that case, a proper evaluation of the fracture resistance under the large cyclic loading conditions becomes necessary. Further systematic study should be carried out on the mutual effects of tearing growth and fatigue growth.