The paper deals with a vibration of the vertical pump during passage through a critical speed. The purpose of this study is calculate the vibration characteristic of the vertical pump. For calculating the vibration characteristic, two methods are given. In the present paper, first, the procedures for calculating the external forces of centrifugal forces from no balancing mass and the hydrodynamic forces which exert on a impeller are presented, using transfer matrix method in case of different environment Secondly the dynamics of unbalanced Jeffcott rotor which through a critical speed are studied in order to consider non linear bearing characteristic and collision between a rotor and a bearing. This dynamic behavior is calculated by the Runge-Kutta method, and effects of system-parameters are discussed. Moreover accuracy of the results of two methods is confirmed by experiment. Finally, From these study it is confirmed that vibration characteristic of verticl pump is improved by means of consideration of non linear characteristics of bearing.