An analytic model for working fluids flowing through capillary tubes has been established with the approximate integral method. All the possible flow regimes in the capillary tubes,including subcooled, two-phase and superheated regimes, are covered in the model, and different analytic solutions are given respectively for each flow regime. As examples, the mass flow rates of refrigerants R12, R134a and R600a through capillary tubes are predicted by the model,and compared with those evaluated by a general distributed-parameter model. The mean bias falls into 1% and the maximum bias is 2.2%, while the computation speed of the new model is more than one order of magnitude higher than that of the distributed-parameter one. An analytic model for working fluids flowing through capillary tubes has been established with the approximate integral method. All the possible flow regimes in the capillary tubes, including subcooled, two-phase and superheated regimes, are covered in the model, and different analytic solutions are As the mass flow rates of refrigerants R12, R134a and R600a through the capillary tubes are predicted by the model, and compared with those evaluated by a general distributed-parameter model. The mean bias falls into 1% and the maximum bias is 2.2% while while calculating speed of the new model is more than one order of magnitude higher than that of the distributed-parameter one.