Neural networks are used to enhance and generalise an Eulerian formulation of inelasticity. The Eulerian formulation means that no history variables, such as plastic strain/deformation or accumulated plastic strain, are used in the formulation, but all state variables are defined in the current state of the material. The Eulerian framework provides a theoretical framework that ensures that such fundamental requirements as frame-indifference and thermodynamic consistency are fulfilled by definition. Neural networks are used to model the rate-dependence and hardening of the material. Both isotropic and directional hardening are enabled. Functional forms for these material properties (visco-plasticity and hardening) are replaced by neural networks. The neural network-based model is applied to both theoretical reference data as well as actual experimental data in the form of stress–strain data. Different numerical formulations of the framework and also different methods for optimising the neural networks are explored. The model is able to reproduce both the theoretical reference solutions as well as the experimental data very well. An implicit FE formulation is also provided in the form of a subroutine (UMAT) in Abaqus. The implementation is applied to 2D and 3D examples, and the implementation seems to be robust and shows nice convergence properties. Overall, the present neural network-enhanced framework seems to be promising and there is potential for further development.