Determination of invariant-plane-strain crystallographic solutions for martensitic transformation between the f.c.c. δ and monoclinic α phases in plutonium alloys, using three possible lattice correspondences and 53 possible lattice-invariant shear systems, identifies the most probable δ-α lattice correspondence. The operative lattice-invariant shear systems are predicted by comparison of both shape strain magnitudes and computed interfacial energies. For the δ → α transformation, twinning on (001)α is favored, giving a (0.817, 0.538, 0.208)δ habit and a [0.947, 0.269, 0.174]δ shape strain of magnitude m1 = 0.324. The α → δ transformation favors slip on (11̄1)[101̄]δ, giving a (0.255, 0.844, 0.471)α habit and [0.822, 0.446, 0.355]α shape strain of magnitude m1 = 0.417. Consideration of the independence of crystallographic solutions as deformation modes indicates that deformation of the monoclinic α phase via α → δ transformation plasticity will require the operation of more than one lattice correspondence, and will likely require additional deformation mechanisms to provide a sufficient number of independent deformation systems to accommodate an arbitrary shape deformation.