In this paper, a new methodology for identifying numerous elastic parameters of an orthotropic material from a single structural test is presented. At the heart of the methodology is the self-learning algorithm which is to extract various stress-strain relationships from a single structural test and train a neural network with the relationships in finite element framework. The constitutive matrix resulting from the trained neural network based constitutive model (NNCM) is compared with the conventional constitutive matrix for an orthotropic material to determine the nine independent elastic constants. An example is given for better understanding of the methodology proposed.