Abstract: This paper deals with the present leak-before-break(LBB) theory around the world,and points out that the LBB failure assessment diagram is suitable for safety assessment and widely applied.A brief description of the application of LBB theory is presented.As for design of pressure vessels,LBB technology is still in an initial stage.Transformation of LBB assessment diagram,stability of the crack propagation and the leak rate are the problems needed to be solved for pressure vessel assessment.The paper points out the direction of LBB technology in the future.