Abstract: This present focuses on the numerical prediction about the cracking growth behavior of circumferential and inclined cracks generally observed in the region of heat-affected zone on the effect of residual stresses of butt-welding of pyrolysis tube.Finite element alternating method (FEAM)based on VNA algorithm combining with finite element modeling was utilized to investigate the effect of residual stress on cracking and predict the cracking growth tendency according to the variation of stress intensity factors along the crack edge.The results show that under the effect of welding residual stresses, the circumferential cracks may tend to circumferentially lengthen along the major axis of crack, and both lengthening along major axis and being deep along minor axis of inclined crack may occur.