Generally, a pumping test requires a lot of effort and expense to perform the test and the drawdown is measured and analyzed for determining the aquifer parameters. The estimated aquifer parameters obtained from graphical approaches may not be in good accuracy if the pumping time is too short to give a good visual fit to the type curve. Yet, the problems of long pumping time and required efforts can be significantly reduced if the drawdown data are measured and the parameters are simultaneously estimated on-line. However, the drawdown behavior of the leaky and unconfined aquifers in response to the pumping may have a time lag and the time to terminate the estimation may not be easily and quickly to decide when applying a parameter estimation model (PEM) on-line to analyze the parameters. This study uses the sensitivity analysis to explore the influence period of each aquifer parameter to the pumping drawdown and the influence period is used as a guide in terminating the estimation when applying the PEM for on-line parameter identification. In addition, the sensitivity analysis is also used to study the effects of different value of Sy and the distance between pumping well and observation well on the influence time of Sy during the pumping.