Using the elastic continuum approach, an energy spectrum and spectral dependences of a group velocities of confined acoustic phonons in planar quasi-two-dimensional nanostructures (nanofilms) of hexagonal symmetry of the 2H-PbI2 type were studied by methods of the theory of elasticity. It is shown that the energy and propagation velocity of vibrational modes for all branches of the phonon spectrum in these type nanostructures are nonlinear functions of a magnitude of a wave vector and a thickness of the nanofilm. The obtained results can be used to analyze an influence of acoustic phonons on a course of phenomena of thermal and electrical conductivity, carrier scattering and optical absorption in nanostructures, components of which are thin layers of lead iodide.