The study of the impact phenomenon on rubber-like materials has been traditionally related to lumped parameter modeling or discrete Finite Element models that require experimentation associated with the material behavior at a level of constitutive modeling, and additional testing to validate their operation in case of engineering applications. This article presents an Artificial Neural Network approach to predict and simulate the low-velocity impact force in a thermoplastic elastomer material. Neural network models were trained and validated with experimental data obtained from impact tests in a modified Charpy apparatus. An experimental setup and a data acquisition procedure were set out to record the impact forces on elastomer specimens. The coefficient of determination R2, the Root Mean Square Error, and the Maximum Absolute Error measures were implemented as error functions to evaluate the performance of the neural networks regarding experimental data. Results show that the proposed method helps to predict and derive impact force curves within the range of the training data, since errors below 1% regarding experimental values were obtained. The results also demonstrate that the neural networks can simulate impact force curves within the range of the experimental values without the need to involve parameters of material strain-rate sensitivity. In addition, the approach was tested in another material, and the corresponding results show good prediction capabilities since errors below 1% were obtained. Therefore, it is concluded that the presented artificial neural models, and the approach, could be useful to create solution spaces for low-velocity impact responses of thermoplastic elastomers.