Abstract
This communication has been dedicated to spectral properties of system composing of periodic arrays of layers which form superlattice with electron effective mass dependent on coordinate inside of each layer. We considered one dimensional model which admits to obtain the exact solution of wave equation. The position dependent mass inside the layer was represented by the linear function. We has found wave functions in their explicit and exact forms as well as the secular equation for the energy eiguen values. The energy spectrum of electrons as expected manifests properties typical for periodic nanostructures.