In this paper, the reliability of welded pressure pipe with circumferential surface crack was calculated by using three dimensional stochastic finite element method. This method has overcome the shortcomings of conservative results in safety assessment with deterministic fracture mechanics method. The calculation of reliability was based on three dimensional elastic-plastic stochastic finite element program which was developed by ourselves. The effects of variables such as fracture toughness, bending moment and the depth of the circumferential surface crack on the structure reliability were also discussed. The calculation results indicate that the crack depth has great effect on the reliability of the welded pipe. When the mean value of the crack depth is changed from 3mm to 7mm, the failure probability of the welded pipe will change from 10-8 to 10-2. The bending moment also has great effect on the reliability of the welded pipe. When the mean value of moment is changed from10000 N.m to 15000 N.m, the failure probability of the welded pipe increases dramatically for the same circumferential crack depth. Irrespective of the changing of moment, the pipe has higher reliability if the crack depth is less than 5mm(a/t<0.5, t is the thickness of the pipe). The method has put forward a new way for safety assessment of welded pipe with circumferential surface crack.