By the Tersoff potential based molecular dynamics (MD) method, the melting and axial compression of the (5,5) C, SiC, and Si nanotubes are simulated, and their molecular configurations, atomic radial distribution functions (RDF) and energy changes during heating-up, as well as their compressive force-strain curves, are obtained. According to the computed results, the differences of the melting and compressive mechanical properties of the three nanotubes are discussed. It is found that the melting C, SiC, and Si nanotubes have netlike, loose spherical and compact spherical configurations respectively, and that the C nanotube has the highest melting point, specific heat, melting heat and load support capability, whereas the Si nanotube has the lowest ones.