Abstract: In this study, we examine the anisotropic effect on elastic interaction between dislocations and general grain boundaries for hexagonal metals; Be Y and Zn. In the setting of the anisotropic linear elasticity in continuous media the calculations of the elastic interaction energy E have been gotten by Head then to be improved by Barnett and Lothe. The dislocations in elastic interaction with a grain boundary in a bicrystal of an elastically anisotropic material are submitted to an image force Fi = - E/d. The results are represented in isoenergy cards on a stereographic projection. The result showed that the interaction energy is inversely depends to the factor of anisotropy H. The maximal energy of interaction is lower then 14 pJ m 1 its always weaker compared to the case of the cubic metals where it is of the order of 100 pJ m 1. The image force can be attractive repulsive or null. The proportion of attracted dislocations depends to the disorientation and the factor of anisotropy H.