Abstract: In this paper,has been discussed the application of FEM to the contact state in the 3D elastic contact problems with the existence of friction and clearance on the basis of the reference.the computational results of the Herz problems have shown a good agreement between the numerical solutions and the analytical ones.As a practical example,this paper uses the abovementioned method to solve the problem of the steam tightness of the cylinder flange coupling in turbines and,therefore,some important conclusions have been drawn.