Vehicle dynamics are dominated by tire forces and their precursor input variables, and a few inertial and suspension properties. Tire forces have been studied since 1930's with the purpose of comprehending and improving vehicle control and handling. Although work has been done on modeling the tire forces using various forms of polynomial interpolation of experimental data, these properties are not thoroughly recognized. As vehicle dynamics' technology improves, the more accurate tire model is required.This paper presents a tire force model by the neural networks. The neural network tire model relates the tire force as a function of vertical load, slip angle, camber angle, and longitudinal force. Many published tire model papers described the side force as Fy(α,γ,Fz)=F(α,Fz)+F(γ,Fz). However, the neural network tire model described the side force as Fy=F(α,γ,Fz) which is closer to the true tire force behavior than the conventional tire model. By teaching experimental tire force data with back propagation, the neural network tire model is established. In order to improve estimation accuracy, a subset teaching algorithm was developed. In all of the operating range, the neural network tire model predicts tire side force within 3% error of measured tire force. A simple vehicle handling simulation is presented which compares performance of the system using the neural network model with that of a conventional polynomial-based model.