This study dealt with deriving an equation of stress-strain relationship developed in the sheet pile subjected to lateral earth pressure on the sand foundation by introducing 3rd order theory. Numerical technique using both 2nd and 3rd order theory was developed in order to predict the displacement of sheet pile. To validate the achievement of the study, the granular soil model foundation tests in which two different sheet piles composed of steel and acryl, respectively, were driven, were performed with the various conditions such as rigidity, free earth or fixed earth end and free earth or anchored earth type. In the range of small lateral displacement of sheet pile, the results by 2nd and 3rd order theory were almost same while the latter proved superior to the former in the excessive displacement.