We propose and investigate two approaches to identify load distributions on a flat panel by using strain measurement values. One approach is an inverse analysis that utilizes the inverse matrix of the load and strain relationship, and the other is a neural network approach that trains a neural network using strains as input and loads as output. For both approaches, we propose a method using a pressure discretization map to represent the load distributions as a set of discrete pressure values. This method makes load identification applicable to load distributions with arbitrary profiles. In order to examine and verify the performance, we conducted numerical simulations and an experiment. Numerical simulation results verified both approaches; however, identification results using the inverse approach were unstable when the strain measurement error existed. On the other hand, the neural network approach showed high robustness to the strain errors by training neural networks with data including artificial strain errors. Based on the results, we discuss the applicability of the load identification approaches.