By using quantum mechanical computer simulations (density functional theory and the method of pseudo-) studied the reaction of small nanoparticles of aluminum (from 2 to 13 atoms), silicon (5 to 18) and zirconium dioxide (18 to 30) in tension and compression. It was revealed that the modulus of elasticity of nanoparticles typically several times higher than the corresponding values for the bulk material. As the number of atoms in the nanoparticle elastic modulus behaves differently for different types of particles with an interatomic bond. In the case of silicon, its value rapidly approaches the value characteristic of bulk material; in the case of zirconium dioxide – almost unchanged; in the case of aluminum – the dependence of the elastic modulus of the size of nanoparticles and non-monotonic determined by the geometry of the particle.