The peculiar effect observed under the indentation of the (001) plane of LiF and MgO single crystals, namely, the sensitivity of the form of dislocation rosettes to the shape of the indenter, is considered. It is shown that the dislocation rosettes being formed around Vickers indentations are symmetrical, while the rosettes around Berkovich indentations are asymmetrical, the edge arms of the dislocation rosettes are different with respect to their length, and the screw arms do not demonstrate such asymmetry. Also, an orientational effect is found under the penetration of a Berkovich indenter, thus, the form of the dislocation rosettes and length of the edge arms change at varying the orientation of the indenter relative to the crystallographic directions of the sample. It is also shown that the asymmetry of the dislocation rosettes is more pronounced on harder crystals and increases with the growth in the load on the indenter. The factors responsible for the anomaly in the development of the dislocation rosettes under nano- and microindentation of the (001) plane of cubic crystals by a Berkovich indenter are found.