The relationship between the strength (σc) of unidirectional fiber-reinforced plastics in different stressed states and the interfacial strength of their components is investigated. The shear adhesive strength (τ0) of fiber—matrix joints determined by the pull-out technique is used as a measure of the interfacial strength. To obtain the correlation curves betweenσc andτ0, the experimental results are used, where both the plastic and adhesive strength change under the influence of a single factor. In this case, such factors are the fiber surface treatment, nature and composition of polymer matrices, and test temperature. It is shown that the strength of the glass, carbon, and boron plastics increases practically linearly with increased interfacial strength. Such a behavior is observed in any loading conditions (tension, shear, bending, and compression). Sometimes, a small (10–20%) increase in the adhesive strength induces a significant (50–70%) growth in the material strength. Therefore, the interface is the “weak link” in these composites. The shape of theσc—τ0 curves for composites based on the high-strength and high-modulus aramid fibers and different thermoreactive matrices depends on the nature of the fiber and the type of stress state. In many cases, the composite strength does not depend on the interfacial strength. Then, the fiber itself is the “weak link” in these composites.