An efficient method is developed to estimate the load level at which a crack occurs on the constituent fiber/matrix interface of a composite subjected to any load. Only the original properties of the fiber and matrix documented in advance or measured independently are required for this estimation, in addition to the transverse tensile strength of a unidirectional (UD) composite made from the same constituent system. Stress concentration factors (SCFs) of the matrix in the composite are crucial for this purpose. Such an SCF cannot be defined following a classical approach, and the SCFs with the perfect and cracked interfaces are derived respectively. Letting the predicted transverse tensile strength of the UD composite with an initial perfect and later cracked interface be equal to the measured counterpart, a critical Mises stress of the matrix at which the crack occurs is obtained. When a Mises stress of the matrix in any other composite made of the same constituents approaches the critical value, the interface cracking load is determined accordingly. Given a fiber and matrix system, whether any further interface modification is necessary and how much potential exists for doing such can be easily understood.