Methodology and equations are developed for maximizing the fundamental frequency (ωf ) of small-amplitude, free flexural vibration of a clamped, rectangular plate consisting of multiple, equal-thickness layers of the same unidirectional filamentary composite material. The synthesis is based on a concise, explicit equation for ωf in terms of plate dimensions, density and the anisotropic flexural and torsional rigidities. The equation is developed in the paper and shown to be quite accurate. Application of the optimization procedure shows that aligned (0 of 90 deg) parallel-ply laminates are the most advantageous. For plate aspect ratios (R) less than unity, 0 deg is optimal, and for R > 1, 90 deg is best. Comparative optimal frequency data are given for plates of three different aspect ratios and constructed of four different filamentary composite materials.