It is shown that the magnetic field dependence of the thermal conductivity of yttrium iron garnet (YIG) can be accounted for if the coupled magnon-phonon modes are employed in calculating the conductivity. On the other hand, the use of independent magnon and phonon modes does not lead to satisfactory agreement between theory and experiment. Experimental results are presented for the magnetic field dependence of the thermal conductivity of YIG in the range of 0.23-1 K.