Localized pipe wall damage accounts for many failures. Numerical modelling of pipes under increasing axial load and constant internal pressure when there is corrosion pits on the exterior surface of the pipe is reported herein. It is shown that for the assumed ideal elastic-plastic material the shape and volume of the plastic field depend on pit depth and its geometry. Pipe wall fracture around a pit can be associated with a critical plastic section. The results reported herein should be relevant for estimating of the risk of perforation and of loss of contents for steel pipes under different loading.