Future increases in gas turbine performance will require numerical algorithms capable of predicting the deformation and rupture of blade materials at elevated temperatures. The current generation of Ni-based superalloys requires constitutive models for rate-dependent plastic deformation of single-crystal turbine blades. Ni-based superalloys show a complicated relationship between temperature and slip on octahedral or cubic slip systems, including softening. A three-dimensional (3-D) finite deformation algorithm is presented for finite element analysis (FEA) of stress and strain histories in anisotropic elastic materials with rate-dependent slip on specific, multiple slip systems. The FEA includes multiplicative decomposition of the deformation gradients, Hencky strain tensor, and Green-Naghdi stress rate with temperature-dependent crystal slip relations to compute finite deformation, slip induced rotations and material softening. Deformation predictions of Ni-based superalloys are compared with experimental measurements and analytical solutions. Good agreement is found, especially when the specimen-to-specimen variations are considered.