The main objective of this study is to investigate the application of the PINN in solution discovery and parameter identification for bending analysis of composite plates considering both Kirchhoff and Mindlin theories. Both forward and backward approaches have been considered. In forward approach, the solution of the bending problem is the main concern where the equilibrium equations and stress-strain relations have been implemented in cost function of PINN to account for the physics behind the problem and the well-known boundary conditions have been considered as the data. For the backward approach, the main idea is to estimate the values of the bending rigidities of the composite plate where the solution of the bending problem is provided for the PINN. The results show that the PINN can accurately calculate the solution for the bending problem and estimate the bending rigidities. To highlight the performance of the proposed PINN, a wide range of numerical results are presented to study the impacts of several architectural factors such as the number of hidden layers and neurons per layer, as well as algorithmic parameters like batch-size, number of epochs, learning rate, and the number of sample points. The results indicate the high importance of each factor so it is crucial to conduct the parametric study to find the best neural network architecture and algorithmic parameters.