The spectral dependences of the coefficients of interband three-photon optical transitions for InSb and for some optical transitions are calculated and a numerical analysis of the coefficient of interband three-photon absorption of light is carried out, which taken into account the contribution to the three-photon absorption of optical transitions occurring during the simultaneous absorption of two photons in the Kane model. Interband three-photon optical transitions in crystals of the InSb and type are classified, and the spectral dependence of some optical transitions is analyzed. The coefficient of linear-circular dichroism of interband three-photon absorption in a crystal in the Kane model is calculated.