Ground response analysis under earthquakes is a critical part of earthquake engineering. Experimental or numerical techniques are commonly applied to implement seismic soil response analysis. However, due to the expensive and time-consuming implementation and also uncertainties in experimental tests and numerical analyses, in this study, deep learning methods are proposed as a good alternative for nonlinear seismic soil response analysis. Long short-term memory network (LSTM) and bidirectional long short-term memory network (BiLSTM) are selected as potential candidates. Input features for the deep LSTM and Bi-LSTM structures are input ground motions at the base of the soil model. And, output features are responses in terms of time series at different locations along the depth of the soil medium. It is noted that all the responses are simultaneously predicted. A limited number of real earthquakes with various characteristics are chosen for training, validation, and testing datasets in the deep learning methods. The datasets are formed by using numerical results. The nonlinear behavior of the soil in numerical models is simulated by employing a sophisticated constitutive model of simple anisotropic SAND (SANISAND). The effectiveness of numerical results is demonstrated with the assistance of the centrifuge test. The results confirm the good performance of the proposed deep learning models for nonlinear seismic ground response prediction. The capacity of the deep learning models is inspected in both the time domain in terms of time series and the frequency domain.