We have studied theoretically galvanomagnetic phenomena in layered conductors of organic origin with multi-sheet Fermi surface being of the form of a weakly corrugated cylinder and weakly corrugated planes. It is shown that in a strong magnetic field H unrestricted growth of the resistivity of such conductors with increasing H is accompanied by forcing current lines out to the specimen surface. The main dissipation mechanism of electron flows is charge carriers scattering by sample boundary even in bulk conductors whose thickness is larger than conduction electrons free path length l. In the case of the specular reflection at the surface the resistivity grows linearly with the magnetic field increasing.