This paper describes the application of finite element method to transient seepage through an earth dam, the stress analysis of an earth dam under a rapid drawdown condition, and the SOR method that we adopted to solve simultaneous equation. We found that apertinent over-relaxation-factor was from 1.4 to 1.6 and an Euclid norm and an arithmetical average are suitable for the convergence judgment. Next, we show a method of transient seepage analysis and a typical example is analyzed here. Furthermore, by a seepage stress analysis at a rapid drawdown, we show that a upstream slope at a rapid drawdown becomes unstability to a considerable degree than that at a steady state seepage.