Electrons in Kane type semiconductor quantum disk in presence of Rashba spin-orbital interaction and external magnetic field parallel to axis of quantum disk are considered theoretically. A three-level model of the kp theory is used to describe electrons in weak Rashba spin-orbit coupling regimes and external magnetic field, taking into account the main features of the band structure in InSb-type semiconductors: a small energy gap, a strong spin-orbit interaction. We calculated the radii, thickness, coupling strength, and magnetic field dependence of Rashba splitting for electrons. It has been seen that the Rashba splitting of the electrons are decreased with the increasing of radius. (C) 2004 Elsevier B.V. All rights reserved.