The pupose of the present paper is to estimate the effects of constraint condition of pile head, ground condition(dry unit weight. $gamma_4$) and embedded pile lengths on the behavior of single pile which is embedded in normally consolidated clay. BBperiment functions can be quantified to these effects obtained from the results of model teats. The ground of model tests is normally consolidated( NC ) clay under three kinds of effective vertical stress. The results of the model tests using the steel pile of two different embedded pile length and of free-head and fired-head show that the lateral load-deflection relationship is to be elasto plastic behavior below $gamma_d/gamma_{dmax}$: 0.84 and that the reduction of lateral load of beyond maximum lateral load($Q_{max}$) at each model test is significantly time-dependent. In this study, it is shown that the displacement relationship can be fitted to exponential function of time by model best results. The effect of ground conditions on the ultimate and yield lateral load is fitted to exponential function including the ratio of dry unit weight to maximum dry unit weight. When tests by results are compared with those from Broms and Budhu et at., the predicted results are over-estimated about 27-87 ayo. In effectivity of constraint condition of pile head on the lateral load-deflection response, the $Q_{fixed}/Q_{gree}-y/D$ relationship is highly non-linear and fitted to parabolic function.