The deep learning steel plastic constitutive model training method was studied based on the recurrent neural network (RNN) model to improve the allocative efficiency of the deep learning steel plastic constitutive model and promote its application in practical engineering. Two linear hardening constitutive datasets of steel were constructed using the Gaussian stochastic process. The RNN, long short-term memory (LSTM), and gated recurrent unit (GRU) were used as models for training. The effects of the data pre-processing method, neural network structure, and training method on the model training were analyzed. The prediction ability of the model for different scale series and the corresponding data demand were evaluated. The results show that LSTM and the GRU are more suitable for stress–strain prediction. The marginal effect of the stacked neural network depth and number gradually decreases, and the hysteresis curve can be accurately predicted by a two-layer RNN. The optimal structure of the two models is A50-100 and B150-150. The prediction accuracy of the models increased with the decrease in batch size and the increase in training batch, and the training time also increased significantly. The decay learning rate method could balance the prediction accuracy and training time, and the optimal initial learning rate, batch size, and training batch were 0.001, 60, and 100, respectively. The deep learning plastic constitutive model based on the optimal parameters can accurately predict the hysteresis curve of steel, and the prediction abilities of the GRU are 6.13, 6.7, and 3.3 times those of LSTM in short, medium, and long sequences, respectively.