Thermodynamic stability conditions for nanoparticles (resulting from non-negativity of the second variation of the free energy) have been analyzed for two cases: (i) a nonvolatile nanosized particle with the size-dependent surface tension; (ii) the limiting case of larger objects when the surface tension takes its macroscopic value. It has been shown that the mechanical stability of a nanoparticle, i.e. its stability relative to the volume fluctuations, is defined by an interplay between the excess (“surface”) free energy and the volumetric elastic energy. According to the results obtained, noble gas clusters and metal nanoparticles satisfy the mechanical stability condition. At the same time, water nanodrops, as well as nanoparticles presented by nonpolar organic molecules, correspond to the stability limit. Among the investigated systems, the stability condition is not carried out for n-Pentane clusters.