A mathematical model of 3-D random road surface was established based on the basic principles of harmonic superposition and triangulated irregular network. A rigid flexible coupling multi-body dynamic model of a heavy truck was established by using SIMPACK software, which included front suspension, rear balance suspension, steering system, tire system, etc. The tires and leaf springs were treated as deformable body, and rubber pads and limit block were reduced to force elements with non-linear stiffness and damping characteristics. Then a ride dynamic model of heavy vehicle was established，which combined virtual prototype vehicle with 3-D random road surface model by using SIMPACK software. The dynamic load coefficient and 95 percentage fourth power aggregate forces were used as the road-friendliness criterions for analyzing the road friendliness of heavy vehicles with different speed. Simulation results indicated that, when the vehicle drove on the B- and C-grade 3-D random road at the speed of 60~90km/h, the road friendliness of mid-axle and rear-axle reduced as the vehicle speed increased. The road friendliness of front-axle didn’t increase as the vehicle speed increased. When the vehicle speed surpassed 80km/h, the road friendliness of front-axle began to decrease. The road friendliness of the vehicle reduced as the vehicle speed increased. The road friendliness of B-grade road reduced by a big margin, while the road friendliness of C-grade road reduced by a small margin.