Mechanical or thermodynamic excitations in solid state physics – phonons, cause all fundamental physical properties of materials and always are present, regardless of what is the main carrier of transport properties and ordering (for example, in electroconductivity, it can be electrons / holes, ions, etc., and in magnetism – magnons). In particular, phonons play a different and more subtle role in low-dimensional nano-scale samples, because they, due to the confinement effects, influence the creation of completely unusual and altered characteristics in relation to large (bulk) samples of exactly the same material. Therefore, the possible phonon spectra and states in model of crystal nanostructures: ultrathin films, nano-wires and quantum dots were founded in the paper. The most noticeable phenomenon is the consequence of the dimensional quantization, but also the shape of the boundary surfaces, as well as the presence of the environment surrounding the nano-pattern. In addition to the analysis of the microscopic properties of the phonon subsystem, the calculation of the temperature dependence of the thermal capacity and entropy of these nano systems was also calculated and performed by comparisons with the same for bulk structure.