Molecular dynamics simulation was used to study and to estimate the effect of thermally resistive mechanisms in non-metallic crystalline solids. The first part of this work focused on line dislocations parallel to the heat flow. At a dislocation density of 1013 cm-2 , edge dislocations caused by an extra half-plane of atoms parallel to the heat flow were found to reduce the thermal conductivity of gallium nitride to 54% of the defect-free value. Using an extrapolation procedure, at dislocation densities of 1012 and 1011 cm-2 , the conductivity was estimated to be 82% and 98% of the defect-free value respectively. For a dislocation density of 2 x 1012 cm-2 , open-core screw dislocations were found to cause a greater reduction, by a factor of about 1.2. These results suggest that, in principle, dislocations parallel to the heat flow can have a significant impact on the thermal conductivity only when the dislocation density is very high.