Abstract: Combining the local load sharing principle，a perfect process of the random crack core evolvement was proposed for unidirectional composites with fibers dist ributed in hexagonal arrays. Based on the perfect process，the probability arithmetic of the random crack core evolvement was deduced，and examples of the random crack core with broken fibers from one to more were carried out. Compared with Markov process，the probability arithmetic of the random crack core evolvement based on the perfect process is accurate enough. Because this arithmetic changes megillah into simpleness，it becomes possible to consider some fiber breaks at the same time in the crack core evolvement process. The result shows that the probability arithmetic of the random crack core evolvement without considering some simultaneous fiber breaks brings marked errors，and computational precisions of the random crack core evolvement probability and composite strength could be enhanced with considering some fiber breaks at the same time.