This chapter explores the use of an artificial neural network (ANN) to obtain the elastic constants of the components of a metal laminated composite material (MLCM). The dataset for the training and validation of the ANN was obtained by applying an analytical model developed for the study of stresses in MLCM. The information used in the dataset corresponds to MLCM configurations and data generated with variants registered in the structural presentation of the inputs and outputs. The best configuration found for the generation of the ANN models yielded an average relative error of less than 4% in relation to the results of the constants evaluated and published in a previous article. As shown in this research, it is important to have a clear definition of the problem as well as an effective selection and preparation of the characteristics of the training data during the constitutive modeling of composite materials and the correct application of the ANN.