The refinement of effective data generation methods has led to a growing interest in using artificial neural networks (ANNs) to solve modeling problems related to mechanical structures. This study investigates the modeling of composite sandwich structures, i.e., structures made up of two laminated composite face sheets sandwiching a lightweight honeycomb core. An ANN was utilized to predict structural deflection and face sheet stress with low computational cost. Initially, a three-point load mode was used to determine the flexural behavior of the composite sandwich structure before subsequently analyzing the sandwich structure using the Monte Carlo sampling tool. Various combinations of face sheet materials, face sheet layer numbers, core types, core thicknesses and load magnitudes were considered as design variables in data generation. The generated data were used to train a neural network. Subsequently, the predictions of the trained ANN were compared with the outcomes of a finite element model (FEM), and the comparison was extended to real structures by conducting experimental tests. A woven carbon-fiber-reinforced polymer (WCFRP) with a Nomex honeycomb core was tested to validate the ANN predictions. The predictions from the elaborated ANN model closely matched the FEM and experimental results. Therefore, this method offers a low-computational-cost technique for designing and optimizing sandwich structures in various engineering applications.