We study the effect of spin-orbit interaction for different shape semiconductor quantum nanostructures. The effective one-band Hamiltonian approximation, the position- and energy-dependent quasi-particle effective mass approximation, the finite hard wall confinement potential, and the spin-dependent Ben Daniel-Duke boundary conditions are considered and solved numerically in this work. The spin-orbit interaction which comes from the spin-dependent boundary conditions is characterized for InAs/GaAs quantum dots and quantum rings. We find it can significantly modify the electron energy spectrum for InAs semiconductor quantum dots and quantum rings built in the GaAs matrix. The energy state spin-splitting strongly depends on the geometry of nanostructures. It has an experimentally measurable magnitude for ultra-small quantum dots and quantum rings with non-zero angular momentum.