This paper presents a road classifier based on the system response with consideration of the tire enveloping. The aim is to provide an easily applicable yet accurate road classification approach for automotive engineers. For this purpose, tire enveloping effect is firstly modeled based on the flexible roller contact (FRC) theory, then transfer functions between road input and commonly used suspension responses i.e. the sprung mass acceleration, unsprung mass acceleration, and rattle space, are calculated for a quarter vehicle model. The influence of parameter variations, vehicle velocity, and measurement noise on transfer functions are comprehensively analyzed to derive the most suitable system response thereafter. In addition, this paper proposes a vehicle speed correction mechanism to further improve the classification accuracy under complex driving conditions. A random forest based classifier is finally trained by treating center spatial frequencies of the octave bands as the classifier input as per ISO-8608. Simulation results validate the proposed approach for various road levels with various velocities, and the overall classification accuracy improved from F-score of 0.7547 (without velocity correction) to F-score of 0.9807 (with velocity correction).