The paper introduces a novel approach for discovering constitutive laws of hyperelastic materials using formal grammars. This method automates the generation of valid constitutive laws and enables data-driven discovery of material models from displacement data with varying noise levels. The approach combines formal grammars with symbolic regression to ensure compliance with physics constraints, both a priori and a posteriori. The methodology is applied to two tasks: generating a library of valid constitutive laws and discovering material models from experimental data. The proposed approach avoids manual feature engineering and human intervention, demonstrating flexibility, efficiency, and robustness in both tasks. For the library generation task, the method efficiently constructs a valid set of constitutive laws. For the data-driven discovery task, it accurately identifies material models, showing strong generalization capabilities. The paper discusses various symbolic regression methods, including Equation Learner, Sparse Regression, Genetic Programming, Deep Symbolic Regression, and Large-Scale Pre-Trained models, highlighting their strengths and limitations. It then proposes a grammar-based symbolic regression approach that incorporates formal grammars and variational autoencoders to generate valid constitutive laws. The method is applied to hyperelasticity, where the material behavior is described by the elastic strain energy density function. The approach involves three steps: library construction, pre-training, and data-driven discovery. The library is generated using a formal grammar, ensuring expressions are valid constitutive laws. The pre-trained model encodes trees into low-dimensional vectors and decodes them back, creating a low-dimensional manifold of tree representations. The discovery step uses gradient-free optimization to find the best-fitting expression. The paper also discusses the properties of formal grammars, including Context-Free Grammars and Regular Tree Grammars, and their application to hyperelastic materials. It outlines the requirements for valid constitutive laws, including thermodynamic consistency, stress symmetry, objectivity, material symmetry, polyconvexity, normalization, growth conditions, and non-negativity. The paper proposes a grammar that enforces these constraints, ensuring generated expressions are valid constitutive laws. The approach is demonstrated using a Neo-Hookean model and other examples, showing the effectiveness of the grammar-based method in generating valid constitutive laws.The paper introduces a novel approach for discovering constitutive laws of hyperelastic materials using formal grammars. This method automates the generation of valid constitutive laws and enables data-driven discovery of material models from displacement data with varying noise levels. The approach combines formal grammars with symbolic regression to ensure compliance with physics constraints, both a priori and a posteriori. The methodology is applied to two tasks: generating a library of valid constitutive laws and discovering material models from experimental data. The proposed approach avoids manual feature engineering and human intervention, demonstrating flexibility, efficiency, and robustness in both tasks. For the library generation task, the method efficiently constructs a valid set of constitutive laws. For the data-driven discovery task, it accurately identifies material models, showing strong generalization capabilities. The paper discusses various symbolic regression methods, including Equation Learner, Sparse Regression, Genetic Programming, Deep Symbolic Regression, and Large-Scale Pre-Trained models, highlighting their strengths and limitations. It then proposes a grammar-based symbolic regression approach that incorporates formal grammars and variational autoencoders to generate valid constitutive laws. The method is applied to hyperelasticity, where the material behavior is described by the elastic strain energy density function. The approach involves three steps: library construction, pre-training, and data-driven discovery. The library is generated using a formal grammar, ensuring expressions are valid constitutive laws. The pre-trained model encodes trees into low-dimensional vectors and decodes them back, creating a low-dimensional manifold of tree representations. The discovery step uses gradient-free optimization to find the best-fitting expression. The paper also discusses the properties of formal grammars, including Context-Free Grammars and Regular Tree Grammars, and their application to hyperelastic materials. It outlines the requirements for valid constitutive laws, including thermodynamic consistency, stress symmetry, objectivity, material symmetry, polyconvexity, normalization, growth conditions, and non-negativity. The paper proposes a grammar that enforces these constraints, ensuring generated expressions are valid constitutive laws. The approach is demonstrated using a Neo-Hookean model and other examples, showing the effectiveness of the grammar-based method in generating valid constitutive laws.