This paper develops the flexible computational model of a heavy truck by interfacing the frame modeled as a flexible body to the heavy truck's computational model composed of rigid bodies. The frame is modeled by the finite element method. Three torsional modes and three bending modes of the frame are considered for the interface of the heavy truck's computational model. The actual vehicle test is conducted off road with a velocity of 20km/h. The vertical accelerations at the cab and front axle are measured in the test. For the verification of the developed computational model, the measured vertical acceleration profiles are compared with the simulation results of the heavy truck's flexible computational model. E grade irregular road profile of ISO is used as an excitation input in the simulation. The verified flexible computational model is used to compare the vibration characteristics of a front suspension system having a multi-leaf spring and that having a tapered leaf spring. The comparison results show that the front suspension having a tapered leaf spring has a higher vertical acceleration at the front axle but a lower vertical acceleration at the cab than the suspension system having a multi-leaf spring.