This dissertation aims to establish a mathematical model to predict the steady-state (stationary) motion of a nano-particle that is suppressed between two parallel moving objects. The main purpose of this study intends to find an appropriate means to reduce surface damage caused by moving nano-paricle. This study will show that, via the molecular dynamics (MD) analysis, the surface will result in different sizes of damaged layer and surface roughness when a nano-particle moves in a distinct way on it. Therefore, it has a significant value in the applications of high precision polishing and surface cleaning to identify the dominant factors in affecting the motion of nano-particle. The proposed model is to find the steady-state motion by meeting the conditions of force and torque balances on a moving nano-particle. Several hypotheses are suggested to derive the interaction force occurred at the interface between particle and each object. The hypothesis starts from the energy point of view. It is claimed that the potential and kinetic energies of object atoms will increase when nano-particle moves relative to the object. Because of the relative motion, some of the object atoms will be pushed or driven away, depending on the manner of motion. The increment of potential or kinetic energies is assumed to be proportional to the number of pushed or driven atoms. The increase of energy is supplied from the works done by the normal stress and shear stress at the interface of particle. The interaction at the front end of particle is very different from that at the rear end when particle rolls on object surface. There is a pushing action at the front end while a pulling action occurs at the rear end. The magnitudes of both actions are dominated and proportional to the adhesive strength between particle and object. The computer simulations show that the particle motion is mainly affected by the relative adhesive strength among particle and two objects. If the adhesive strength between particle and one object increase, the particle will increase the sliding speed relative to another object. On the other hand, if the adhesive strength between particle and one object is close to that of another object, the particle tends to have significant rolling motion relative to two objects. The suppressed loading between particle and objects has little effect on the qualitative trend of particle motion. The validity of proposed model is evaluated by the molecular dynamics simulation. It indicates that the predicted behaviors of proposed model are consistent with that from the analysis of molecular dynamics simulations.