The research of nanoscale contact problem has important significance for the micro-/nano-machinery, especially for micro-/nano-contact problem of material defects, from which deformation and failure mechanism of materials could be revealed. Molecular dynamics method is a valid approach that describes microscopic phenomenon. Taking the rigid hemispherical surface in contact and indentation process with the perfect and defective monocrystalline copper as the research object, the molecular dynamics model of nanoscale contact was established, after solving and simulating analysis. Results showed that the substrates above the square void collapse at contact depths of 0.20 and 0.37 nm when the depths of the square void (d) are 0.8 and 1.6 nm, respectively. The dislocations and glide band increase as the d increases; at the same time, a larger depth of square void results in a bigger contact force between the hemispherical surface and the substrate surface. In the process of disengagement, there is a sudden drop in the contact force, and unrecoverable plastic deformation of the copper material occurs. Moreover, with the increase in void depth, the number of high-stress atoms increases between the hemisphere and the surface of substrate. The stress is mainly distributed in the diagonal of the square void, and the contact area generates stress concentration.