The inclusion problem of linear isotropic elasticity is applied to ana
lyze the elastic strain energies of coherent, semicoherent and incoher
ent needle-shaped inclusions. Misfit strains of a general tetragonal t
ype, elastic constants and orientation of the needle are treated as va
riables. The strain-energy minimization criterion is adopted to find t
he optimum orientation. Several new and general conclusions are derive
d for the elastic state of the needle inclusions. The predicted optimu
m orientation is compared with that obtained by the purely geometrical
invariant-line criterion. It is found that the two criteria predict t
he identical orientation only under special cases.