A perfect evolvement process of random crack cores is presented and a random crack core model for predicting the longitudinal tensile strengths of unidirectional composites is built in this paper. Based on the crack propagation rules, the numerical relationship of the number of random crack cores, evolvement probability of a random crack core evolving to critical size, and failure probability of a unidirectional composite are deduced. With considering some fibers breaks simultaneously and the influenced-length of the random crack cores increasing with the number of broken fibers, evolvement probability algorithms of a random crack core are developed based on the perfect evolvement process. At last, the longitudinal tensile strengths of unidirectional composites are predicted by the random crack core model, and the result shows that the random crack core model is more accurate than the classical theoretical models.