The existing design of the pumping systems mainly focuses on the approximate computational formulae and procedures,which are developed based on the analytic approaches of conventional oil/gas fields.The calculation of polished rod loads usually just concerns about the static and inertial loads.And the computation of gearbox torque generally uses empirical formulae and correction factors.The above modeling procedures,if applied to the coalbed methane(CBM) wells,can not give the desired accuracy of the system design and its pertinent analysis.In this paper,based on the kinematic and dynamic analysis of the pumping system,the kinematic relation of polished rod is analyzed,and the variation of the total loads of polished rod is developed with the limits of CBM well conditions along the string.The gearbox torque calculation model is established by combining the counterbalance effect with the calculated dynamometer cards and torque factors.The application characteristics of this model are demonstrated by the example of ZH002-4 well in Qinshui basin.The interpretations of results show that the cranks of beam units should rotate in a counter clockwise direction viewed with the wellhead to the right.Compared with oil?gas fields,the dynamic and friction to polished rod load ratios are relatively high and the computation of polished rod loads should involve the static and inertial loads,as well as vibration and friction loads.And the dynamic load ratio decreases rapidly during the production.Besides,the total deformation of the string is small in CBM wells.As for balanced operation,the gearbox torque load usually has two approximately equal peaks and the magnitudes of instantaneous torque are just within 50% of unbalanced gearbox loadings.The proposed research improves efficiency of the pumping system,loads the pumping unit more uniformly,and provides the reasonable basis for selecting the units. The existing design of the pumping systems mainly focuses on the approximate computational formula and procedures, which are developed based on the analytic approaches of conventional oil / gas fields. The calculation of polished rod loads usually just about the static and inertial loads .And the computation of gearbox torque generally uses empirical formulae and correction factors. the above modeling procedures, if applied to the coalbed methane (CBM) wells, can not give the desired accuracy of the system design and its pertinent analysis. In this paper, based on the kinematic and dynamic analysis of the pumping system, the kinematic relation of polished rod is analyzed, and the variation of the variation loads of polished rod is developed with the limits of CBM well conditions along the string. gearbox torque calculation model is established by combining the counterbalance effect with the calculated dynamometer cards and torque factors. the application characteristics of this model are de monstrated by the example of ZH002-4 well in Qinshui basin. The interpretations of results show that the cranks of beam units should rotate in a counter clockwise direction viewed with the wellhead to the right. Compared with oil? gas fields, the dynamic and friction to polished rod load ratios are relatively high and the computation of polished rod loads shall involve the static and inertial loads, as well as vibration and friction loads.And the dynamic load ratio decreases rapidly during the production.Besides, the total deformation of the string is small in CBM wells.As for balanced operation, the gearbox torque load has two approximately equal peaks and the magnitudes of instantaneous torque are just within 50% of unbalanced gearbox loadings.The proposed research improves efficiency of the pumping system, loads the pumping unit more uniformly, and provides the reasonable basis for selecting the units.