The electronic states of a Kane-type cylindrical cavity with and without magnetic field are theoretically investigated. The eigenvalues and eigenstates of the Kane's Hamiltonian are obtained. Calculations are performed for a hard-wall confinement potential and electronic states are obtained as a function of the magnetic field applied along the cavity cylinder axis. The size dependence of the effective g-value in bare InSb cavity cylinder for electrons are calculated. It has been seen that the effective g-value of the electrons are decreased with a decrease is the cavity cylinder's radius. (c) 2005 Elsevier B.V. All rights reserved.