  Results are presented for finding the optimal orientation of an anisotropic
elastic material. The problem is formulated as minimizing the strain energy
subject to rotation of the material axes, under a state of uniform stress. It
is shown that a stationary value of the strain energy requires the stress and
strain tensors to have a common set of principal axes. The new derivation of
this well known coaxiality condition uses the 6-dimensional expression of the
rotation tensor for the elastic moduli. Using this representation it is shown
that the stationary condition is a minimum or a maximum if an explicit set of
conditions is satisfied. Specific results are given for materials of cubic,
transversely isotropic (TI) and tetragonal symmetries. In each case the
existence of a minimum or maximum depends on the sign of a single elastic
constant. The stationary (minimum or maximum) value of energy can always be
achieved for cubic materials. Typically, the optimal orientation of a solid
with cubic material symmetry is not aligned with the symmetry directions.
Expressions are given for the optimal orientation of TI and tetragonal
materials, and are in agreement with results of Rovati and Taliercio
\cite{Rovati03} obtained by a different procedure. A new concept is introduced,
the strain deviation angle, which defines the degree to which a state of stress
or strain is not optimal. The strain deviation angle is zero for coaxial stress
and strain. An approximate formula is given for the strain deviation angle
which is valid for materials that are weakly anisotropic.
