A theory describing a spin-dependent transport of electrons through a thin metallic nonmagnetic layer sandwiched between two ferromagnets is developed in the ballistic regime and current-perpendicular-to-plane (CPP) geometry. The theory is based on the Landauer formalism and the transmission amplitude for the electron Bloch waves with an arbitrary dispersion law travelling from one ferromagnet to another through a nonmagnetic spacer. The semi-classical (nonoscillating) part of the magnetoresistance (MR) ratio is considered in the effective-mass approximation for the sandwich band structure. The parameters defining the value of the MR ratio are obtained. It is shown that the electron specular scattering on the interfaces may be the cause for the giant magnetoresistance (CPP GMR) effect. The influence of the electronic structure on the MR ratio has been numerically studied in the effective-mass approximation.