We calculate the ground and excited electron and hole levels in spherical Si quantum dots inside SiO₂ in a multiband effective mass approximation. The Luttinger Hamiltonian is used for holes, and the strong anisotropy of the conduction electron effective mass in Si is taken into account. As the boundary conditions for the electron and hole wave functions, we use the continuity of the wave functions and the flux at the boundaries of the quantum dots.