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The new expression for the three-phonon scattering relaxation rate r g , = ( B , + B , e-OlaT) x x g(w) Twl proposed by Dubey and Misho is used to calculate the lattice thermal conductivity of InSb and GaAs in the entire temperature range 2 to 300 K and 2 to 800 K, respectively and very good agreement is obtained between experimental and calculated values of the phonon conductivity of both the samples, InSb and GaAs, in the entire temperature range investigated. The reduced contribution due to transverse and longitudinal phonons are also studied by calculating the separate contribution due to each mode of phonons. The percentage contributions of threephonon normal and three-phonon umklapp processes are studied. A comparative study of present results with the results obtained by previous workers is also made for both of the samples.