Abstract: Based on the model of hard sphere, the computer simulation of particles of the two-dimensional nearly independent particle system is reported in accordance with mechanical laws. In the simulation, multi-measurement are taken on the energy and speed of particles of the system at different time. The statistical average is performed over the results of measurements. The distribution diagrams of particles against their energy and speed in the mechanical system, with different number of particles, are obtained, and hence the universal distribution function is acquired. This completely proves that the long-term behavior of mechanical system that consists of a few particles has definite statistical law.

Key words: nearly independent particle system, statistical law, computer simulation, Maxwell distribution