Advances in high technologies using nanometer-size structures, such as thin films and carbon nanotubes, requires calculation of mechanical properties for the objects of the nanosize scale level. Majority of the theoretical mechanical models for nanoobjects is based on the macroscopic equations of theory of elasticity. This gives the questions about applicability of the quantities obtained from the macroscopic experiments to the nanoscale objects or about necessity of corrections taking into account the scale effects. The presented paper is devoted to 1) theoretical investigation of the influence of the scale effects on the Poisson's ratio, Young modulus and the bending stiffness of a nanocrystal, which is extended in one direction and has a limited number of atomic layers in another direction, 2) theoretical investigation of the delamination processes of a preliminary stressed bi-layered plate from a rigid foundation, 3) creation of stable models for crystal lattices.