Molecular dynamic modeling was used to study the interactions between nanometer size two-dimensional particles in proximity to the surface of a two-dimensional crystal composed of the same material. The modeling was conducted by using triangular lattices of atoms that interact through a Lennard-Jones potential. The atoms were configured such that the particle consisted of a circle with 463 atoms. The crystal was in the shape of a rectangle and contained 442 atoms. The system was assumed to have periodic boundary conditions. It was first allowed to equilibrate with an assumed dimensionless kinetic energy per atom of 0.2 epsilon. Subsequently, the particle was made to approach the surface at a velocity of 0.387 sigma/t (corresponding to 6.25 m/s for argon), which is small compared with the speed of sound in the material. The approach was conducted in two modes:(1) centroidal displacement control at constant temperature and (2) free flight at the same intercentroidal velocity of approach. For each case, the intercentroidal distance, velocity, and forces were determined as the particle approached, made contact, and relaxed into the surface. The computation followed the response of the system for a total of 11900 iterations (corresponding to 2.54 ns for argon). The particles and surfaces were found to deform before, during and after impact. Surface forces were sufficiently large to prevent the particles from separating from the substrate following the collision. The excess energy generated acoustic waves and lattice defects. The geometry of the system at selected times was used to illustrate the deformations that occur. Results based on a molecular statics approach are also presented for comparison with analytical models based on potentials. Finally, preliminary results of a particle being removed from the substrate are presented.