Abstract: Deep learning has become increasingly popular in the engineering profession as computer technology has advanced. However, the data set used for training frequently has the characteristics of a small sample set, of a high dimension and sparse in practical application, limiting the application breadth of standard deep learning models. In this study, a transfer learning enhanced physics-informed neural network is developed to solve the forward and inverse mechanics problems with the sparse data set. The physics-informed model, when used in conjunction with the transfer learning method, improves learning efficiency and maintains predictability in the target task by using existing information from the source model without requiring a large amount of data. The method starts by using a data set to train the source model of a thin plate (simple support at both ends and fixed support at both ends). The features of neural network are retrieved from the source model based on deep transfer learning. The source model is fine-tuned by using the sparse data set in the target task. The target task of response prediction (forward problem) and boundary recognition (inverse problem) in the thin plates with different boundaries are verified. The results show that the method has high accuracy and generalization ability for the target task with a small sample set. Compared with the single data-driven deep learning method, the physics-informed deep transfer learning has the advantage of avoiding the cost and grid independence caused by data generation.