Using the molecular dynamics method, a study of the compression deformation of nickel nanoparticles with amorphous and nanocrystalline structures at low temperatures was conducted. The influence of the size of nanoparticles on their strength and on the strain value at which maximum stress is reached has been investigated. The characteristics of deformation behavior in the case of amorphous and nanocrystalline nanoparticles were identified. It was shown that as the size of the nanoparticles decreased, both for amorphous and nanocrystalline types, their strength increased. The strength values for nanocrystalline nickel particles were approximately twice as high as those for particles with an amorphous structure. With decreasing particle size, the strain value at which maximum stress was reached during compression of the nanoparticles also increased. One possible reason for the influence of particle size on its strength in the case of an amorphous structure may be densification and partial crystallization of the structure near the load application sites. Partial crystallization in the contact patch regions during compression of amorphous nanoparticles was observed in the model in most cases. During compression of particles with a nanocrystalline structure, frequent phenomena included grain rotation and grain boundary sliding. As with amorphous nanoparticles, the phenomenon of structural densification near the contact patches and its reorientation were observed, such that the most densely packed atomic planes of the (111) type became parallel to the contact patch plane.