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In this paper, the strain-based and stress-based methods for solving optimal orientation problems of orthotropic materials are studied. Closed form solutions for both methods are derived and classified. The optimal orientation of both shear “weak” and some shear “strong” orthotropic materials may coincide with the major principal stress direction in the stress-based method. Similar results from the strain-based method are also derived. From the derivations, however, it can also be shown that both methods may fail under a special condition called “repeated global minimum” condition.