Neural networks (NNs) based constitutive modelling to extract stress–strain relationships from data have recently gained significant attention, driven by advancements in artificial intelligence. However, a generic NN that can directly extract new inelastic constitutive models from experimental data is still lacking. Additionally, integrating NN models into numerical simulations for boundary value problems (BVPs) while ensuring computational stability and efficiency presents a considerable challenge. This study proposes a novel postulate‐driven NN (PNN) that leverages the basic constitutive modelling postulates of inelasticity and the strong nonlinear fitting ability of NNs to identify internal variables and constitutive relationships from stress–strain data automatically. The feasibility of PNN is demonstrated by successfully identifying internal variables and stress–strain responses in theoretical models of von Mises elastoplasticity and isotropic elasticity‐based damage, as well as real‐world clay experiments. The developed model is subsequently embedded into the finite element method (FEM) for solving BVPs by feeding the predicted stress and updated material tangential matrix. In particular, the PNN‐based damage model is encoded into FEM to simulate bar damage. The results indicate that PNN is a promising alternative to directly identify internal variables and constitutive relations from experimental stress–strain data. Furthermore, its integration with FEM enables an efficient solution of BVPs while maintaining computational stability and cost‐effectiveness.