Hashin–Shtrikman bounds are given for the effective bulk and shear moduli of randomly oriented aggregates of materials with trigonal (crystal classes 3, 3¯) and tetragonal (classes 4, 4¯, 4m) symmetry. The Hashin–Shtrikman bounds are narrower than the widely used Voigt and Reuss bounds by factors of 2–13. This study completes the development of explicit Hashin–Shtrikman bounds for polycrystals of all crystal symmetries and classes, except triclinic.