When a bicrystal or polycrystal are subjected to a change in temperature, the individual responses of the two adjoining crystals may differ in a manner, which tends to produce a dilatational mismatch along grain boundaries. If compatibility is to be retained along the interface, an additional set of stresses must then be generated in order to conserve this compatibility. ‘Compatibility stresses’ will also be generated whenever a polycrystal is heated or cooled and the thermal expansion coefficients of the individual grains are different due to thermal expansion anisotropy. In such cases adjacent grains will attempt to change dimensions and develop mismatches by amounts controlled by the parameter Δa*ΔΤ, where Δa is the difference between the thermal expansion coefficients in the appropriate directions, and ΔΤ is the temperature change. These ‘compatibility stresses’ may be relieves if grain boundary motion, triple junction migration and grain growth are possible. These ‘compatibility stresses’ may play important role in the kinetic behavior of the microstructure ranging from influencing the behavior of lattice dislocations near the grain boundaries to promoting grain boundary and triple junction dragging or moving. The motion of the ‘special’ grain boundaries, triple junctions with ‘special’ grain boundaries and twins under the influence of internal mechanical stresses is the main subject of this paper.