Simulation of linear elasticity problems is widely applied in mechanical and architectural engineering, and surrogate models driven by sample data have become an effective approach to perform fast simulation. However, due to the scarce and expensive data in engineering, traditional data-driven surrogate models suffer from low accuracy. This paper proposes a new Physics Informed Surrogate Model (PISM), with the objective to accelerate the numerical simulation of linear elasticity problems. The governing equations are incorporated into the training process of neural networks as effective supplement information to sample data, which improves the prediction accuracy of surrogate models in small data scenarios. A ResNet structure is introduced to further improve predicting performance of the model. Experimental results show that the prediction accuracy of PISM is significantly higher than that of pure data-driven surrogate models under small data conditions, and the solving speed reaches 8–9 times that of the finite element method.