The processes are mutually inversed and can be described by the same mathematical model. The two physical processes are generally called one point lifting and lowering. In the processes a pipeline is lifted up from the seabed to the sea surface or put down to the seabed from the sea surface by joint A. The sketch of the pipeline abandonment and recovery operation is shown in Figure 1. So the mathematical model of pipeline abandonment and recovery should be established. The calculation of these quantities is very useful to guide the operation. During the process the pipeline’s axial forces, bending moments must be controlled in a reasonable scope to prevent its strength damage. In the abandonment operation the A&R cable lowers a pipeline down to the seabed by a pull head and in the recovery operation lifts it up to the sea level. To do the mechanical analysis the mathematical model is a very important problem. In offshore oil and gas engineering the pipeline laying engineers need to do detailed mechanical analysis to determine the operation parameters and then make sure that the pipeline will not overstress during the operation. Introductionīad weather is frequent during laying offshore pipelines, so the pipeline abandonment and recovery operation is unavoidable. Finally, an approximate formula for quick calculation of the suspended pipeline length is proposed based on Buckingham’s Pi-theorem and mathematical fitting. The results of the presented method are in good agreement with the results of the traditional finite element method coupled with contact analysis. Based on a traditional numerical method, the problem is solved directly by the proposed technique. A novel technique for the handling of the moving boundary condition is proposed, which can tackle the moving boundary condition without contact analysis. The mathematical model of pipeline abandonment and recovery is a moving boundary value problem, which means that it is hard to determine the length of the suspended pipeline segment. For this problem a third-order differential equation is used as the governing equation in this paper, rather than the traditional second-order one. In offshore oil and gas engineering the pipeline abandonment and recovery is unavoidable and its mechanical analysis is necessary and important.