The present paper discusses the estimation of the road friction coefficient based on the brush model. This popular tire model is reanalyzed beginning from the conventional physical model, following which intrinsic expressions are derived. The grip margin that is defined as the residual tire force normalized by the radius of friction circle is estimated using the tire forces and self-aligning torque. A cubic equation is obtained as the grip margin equation for the isotropic model. The anisotropic model results in a quintic equation whose numerical solution is approximated by Chebyshev polynomials. The estimation method is verified by a numerical simulation using CarSim, a popular vehicle simulation software. The estimated friction coefficients are found to agree with the assumed values in the case of smaller grip margins, especially in lower friction conditions.