A generalized expression is used on the basis of relaxation time approximation to facilitate calculation of lattice thermal conductivity of dielectric materials as well as skutterudite family consists of compounds of the form AB 3 . It is assumed that phonon scattering processes are independent and is represented by frequency dependent relaxation times. The contributions of normal three phonon scattering processes are included explicitly as redistribution of phonon momentum between two oscillation branches is considered. Magnitudes of relaxation times are estimated from the experimental data. The result for CoSb 3 is in reasonably good agreement with the experimental result in the temperature range 1-1000 0 K. It is observed that redistribution of phonon momentum between two oscillation branches leads to a significant suppression of thermal conductivity maximum and it is observed that for unfilled skutterudite the main dominant mechanism at the thermal conductivity maximum is three phonon normal scattering process.