Composite materials facilitate the control of specific properties in components while varying the type, angle, and order of individual fiber weaves in the laminate. This possibility of synthesizing material properties has aroused great interest in musical instrument making since the availability of synthetic fiber composites in the 1970s. However, when arranging plies, the combination of weave types and angles can lead to vibroacoustic effects which are unusual for makers used to working with wood. The mechanics behind these effects are described, starting with an outline of the theory of vibrations in thin plates. Further, the consequences of rotating fibers are theoretically derived and, subsequently, examined in a series of measurements on rectangular thin plates as well as assembled violin top plates. From the findings obtained, it can be concluded that the specific characteristics have to be taken into account for a successful use of composite materials in musical instrument making. This paper, therefore, concludes with easy-to-understand recommendations for musical instrument makers when using fiber composites.