Bounds on the effective elastic moduli of randomly oriented aggregates of orthorhombic crystals have been derived using the variational principles of Hashin and Shtrikman. The bounds are considerably narrower than the widely used Voigt bound and Reuss bound. In many instances, the separation between the new bounds is comparable to, or less than, the uncertainty introduced by experimental errors in the single‐crystal elastic stiffnesses. The Voigt‐Reuss‐Hill average lies within the Hashin‐Shtrikman bounds. several percent.