Abstract: In repairing the casing damaged wells, it occurs frequently that drill strings are stuck. Therefore, it is necessary to judge the positions of free points of the drill strings. In order to find the theory basis of estimating the sticking positions, the mechanical behaviors of drill strings in casing pipes have to be learnt. It is very difficult by normal methods to depict the states of stress and strain when they work in a few kilometers in oil wells or water wells. However, for vertical wells, finite element methods (FEM) can solves the difficulties above. Based on the relation between the lifting force and the displacement of the drill string calculated by FEM, the field engineers and technicians can judge accurately the position of the free point of a drill string and get rid of the problem. The target of the paper is to simulate a pipe string of a vertical well with FEM. By the analysis of results of FEM, the mechanical behavior of drill strings in casing pipes can be learnt well. It is the basis of judging the positions of free points of drill strings.

Key words: Finite element analysis, Free point, Stuck