We propose a finite element method to investigate the phenomena of shock wave and to simulate the hydrodynamic model in semiconductor devices. An introduction of this model is discussed first. Then some scaling factors and a relationship between the changing variables are discussed. And then, we use a finite element method (P1-iso-P2 element) to discrete the equations. Some boundary conditions are also discussed. Finally,a sub-micron n+-n-n+ silicon diode and Si MESFET device are simulated and the results are analyzed. Numerical results show that electronic fluids are transonic under some conditions.