Particle penetration through a square potential and a step potential barrier are studied with the eight-band Kane Hamiltonians. It has found expressions for transmission probability and reflection coefficients of electrons for both potentials. It is shown in the Kane model that the transmission probability will have a finite value that is different from the one-band model at the state where the barrier height is infinite. The Landauer formula for resistance is applied to the Kane type semiconductor heterostructures. (c) 2005 Elsevier B.V. All rights reserved.