Metal rubber (MR) is an entangled fibrous functional material, and its mechanical properties are crucial for its applications; however, numerical constitutive models of MR for prediction and calculation are currently undeveloped. In this work, we provide a numerical constitutive model to express the mechanics of MR materials and develop an efficient finite elements method (FEM) to calculate the performance of MR components. We analyze the nonlinearity and anisotropy characteristics of MR during the deformation process. The elasticity matrix is adopted to express the nonlinearity and anisotropy of MR. An artificial neural network (ANN) model is built, trained, and tested to output the current elastic moduli for the elasticity matrix. Then, we combine the constitutive ANN model with the finite element method simulation to calculate the mechanics of the MR component. Finally, we perform a series of static and shock experiments and finite element simulations of an MR isolator. The results demonstrate the feasibility and accuracy of the numerical constitutive MR model. This work provides an efficient and convenient method for the design and analysis of MR components.