The empirical Gaussian-based mathematical model of soil displacement increment under the traveling wheel was extended to be applicable to any depth of soil layer under the ground contact surface of the wheel. The unknown coefficients were obtained by least mean-square fitting with the soil displacement curve measured through laboratory sophisticated soil bin test. Then those coefficients were re-derived as a function of depth. The movement of soil particles at the ground contact surface was modeled by dividing into 2 kinds; first, the free movement of soil particles before contact with the wheel and the movement of the particles after they are separated from the wheel surface and the second type represent soil movement during attachment to the wheel surface. By combining the models for the ground contact surface of the wheel with that for all soil layers, the extended model that can describe soil displacement increment in both the vertical and horizontal directions using one equation was established. The predicted results obtained using the extended model fitted quite well with the measured values. The predicted strain increment distributions show the same trends as the measured distributions.