At present there is a growing amount of concepts and proposal suggesting potential functionality of spin degrees of freedom and of spin-polarized electronic characteristics. The spin-orbit interactions (SOI) in semiconductorS form the basis of the major proposals for new semiconductor spintronic nanostructures. SOI being the major attribute of topological insulators, which leads to the band inversion of the conduction and valence edge states and topologically nontrivial regime of electronic states, it is obviously to expect new unusual peculiarities of electronic states in the quantum well and tunnel layered nanostructures. Some of such features are analyzed in the present paper. The model Hamiltonian of electronic states of most topological insulators isformulaare the Pauli matrices. The influence of the electrical polarization u = {0,0,u} r (or shear deformation) on the structure spectrum through the sublattices displacement is described by the last terms in the non diagonal blocks.In the topological insulator state Eg is negative parameter. Tunnel characteristics of barrier structure can be analyzed on the basis of one band approach. Neglecting the quadratic and cubic terms, excluding the valence band from full Hamiltonian (1) and considering free motion along of in-plane direction we obtain the 2x2 HamiltonianformulaThe evolution of quantum well states of the topological insulator structures as well as tunnel characteristics of the barrier structures are analyzed for different parameter configurations. As illustration in Fig.1 the spectrum of so called induced topological states in quantum well structure are plotted. Fig.2 ilustrates the effect of spin filtering of topological barrier structure.Using standard technique we obtain the transmission coefficient C T and the tunnelling time TformulaQuantum well topological states are obtained on basis of two band symmetrical model.The dispersion relations for topological states of the well with thickness 2a isformulafigure