This paper analyses the discrete hydraulic systems with emphasis on hydraulic parameter analysis for a pump-turbine power plant. The developed model could make hydro-electric power plants transient behavior studies more easy and accurate, especially for complicated systems. The simulation was developed based on analog mathematical models of transient phenomenon equations (Hydroacoustic modeling). In this method, the governing equations for transient flows are solved based on equivalent electrical circuits being defined for different equipments of the system. By using the Kirchhoff's voltage law for the final equivalent circuit of the system a set of nonlinear ordinary differential equations is generated. The unsteady friction loss and visco-elastic behavior of pipe and fluid are considered in the pipelines model. A set of nonlinear ordinary differential equations is generated by using an implicit scheme. These equations of nonlinear ODEs are solved using a fourth order Runge-Kutta method. Further validation has been carried out with experimental values. Also a mathematical model for Francis pump-turbine has been developed and the transient behavior of two different cases of hydraulic systems including the pump-turbine has been investigated. The results were logically correct and acceptable. This method is very efficient for overall simulation of hydro power plants including turbine, generator and transformer.