Abstract: This paper is a development of the quadratic strength criterion of integrated modes for fiber-reinforced composite materials. For simplification of evalution, the Cubic terms of the strength criterion in the reference [1] is neglected. From the point of view of principle, the criterion that includes the cubic terms has better accuracy, but it is not the truncating cubic tensor polynomial expansion. The criterion is mathematically expressed in a general cubic equation in terms of stress invariants. Considering two basic failure modes of unidirectionally fiber-reinforced composites, the criterion can be simplified. Two methods for determining cubic coupling coefficients are discused. This criterion has the characteristics more rational and simpler than that in the reference [4], and agre-es better with experimental data.