Properties of nanostructures related to the phonon physics are of major current interest due to a broad range of modern applications and new directions of research, in particular, on nanomechanical resonators, phononic crystals, and ultrasensitive sensors. Confinement of the propagation medium for mechanical vibrations modifies, also on a qualitative level, the properties of phonons including their interaction with electrons, photons, magnons etc. [1,2]. Thus, there are well known classical results related to confinement and based on the linear elasticity theory, e.g., for the modes determined by the existence of a surface or of an interface within a massive material (Rayleigh, Love, Stoneley) as well as for the oscillation modes of an elastic plate (e.g., Lamb). Nevertheless, application of this theory to nanostructures remains an open issue which raises new questions [3]. I will present an approach to the description of quasi two-dimensional nanostructures (membranes, thin films, layered nanomechanical resonators) when the wavelength may be comparable to their thickness. The approach is slightly different form the ones commonly used (like the method of potentials or the method of partial waves) and leads to some new analytic and numeric results important for understanding the role of surface effects.