Predicting the non-linear loading response is the key to the design of suction caissons. This paper presents a systematic study to explore the applicability of deep learning techniques in foundation design. Firstly, a series of three-dimensional finite element simulations was performed, covering a wide range of embedment ratios and different loading directions, to provide training data for the deep neural network (DNN) model. Then, hyper-parameter tuning was performed and it is found that the basic Fully-Connected (FC) neural network model is sufficient to capture the non-linear response of suction caissons with excellent accuracy and robustness. Furthermore, the optimized FC neural network model was also successfully applied to a database of suction caissons in sand, demonstrating its broad applicability. By comparing three typical DNNs, i.e., FC, Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM), it was observed that the FC neural network model excels over others in terms of simplicity, efficiency and accuracy. More importantly, by looking into the model's generalization performance, the FC neural network model can also identify the change in foundation failure mechanisms. This study demonstrates the DNN's powerful mapping ability and its potential for future use in offshore foundation design.