A realistic soil layer consists of remarkably nonlinear medium with hysteretic characteristics. Such a soil medium has a strain dependent behavior on rigidity and damping. The order of strain level of the ground subjected to strong earthquake motion is (10)^<-4> to (10)^<-2>. It is indispensable to estimate the nonlinear dynamic behavior of soil layer under strong earthquake, corresponding to strain dependent rigidity and hysteretic characteristics. By step-by-step integration technique, the motion of discrete lumped mass system for a soil layer is solved. The surface motion in maximum displacement, acceleration and amplification factor in time domain is obtained. The response spectra and Fourier spectra of surface waves are also analysed. The typical properties of nonlinear dynamic response of the ground are pointed out.