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In response to the need for management system of the pressure vessel of gathering and transportation in the offshore oil platform,the pressure vessel with oblique nozzles was researched by using Ansys and the local notch stress and strain approach.The computational methods for predicting the lifetime crack initiation and reliability was given. The lifetime crack initiation and reliability results of 60 degree-oblique nozzle was obtained in order to accomplish an example. The region of crack initiation was researched. The various dimensionless structural parameters affecting the lifetime crack initiation, which are the angle of inclination,the ratios of nozzle diameter / shell diameter,the ratios of shell thickness / nozzle thickness,the ratios of shell diameter /shell thickness,was studied. These research show that the local notch stress and strain approach which needs strain data of material and structural fatigue notch factor and structural stress-strain loading history can apply to predict the lifetime crack initiation and reliability of the real weld effect and the combined effect of multiple load to oblique nozzle. In the simple FEM models the region of crack initiation occurs at the crotch corner in the meridional direction of the cylindrical shell. The result narrow the search scope to cracks in real situation. The lifetime crack initiation is decreased with the smaller angle of inclination,the larger ratios of nozzle diameter / shell diameter,the larger ratios of shell thickness / nozzle thickness,the larger ratios of shell diameter / shell thickness.The results of the lifetime crack initiation is remarkably decreased when the angle of inclination is 30 degree. Considering the local notch stress and strain approach with inherent dispersion,the proposed approach which predicts the lifetime crack initiation with certain reliability is a simple and effective method. The research results can provide some referential value in order to formulate and optimize maintenance strategy of the pressure vessel of gathering and transportation in the offshore oil platform.