Summary: The non-uniqueness of the transition from nonobjective constitutive relations to objective ones with the use of the principle of material frame-indifference is shown. To eliminate it, the concept of finite strain without rotations (FSWR) for a given material type and each strain component (elastic, plastic) is introduced. In FSWR the rotation is excluded with respect to the natural preferred configuration for a given material. Considered are a simple solid, a liquid, a monocrystal, a polycrystal and a composite. The procedure is proposed for consistent generalization of known infinitesimal relations for finite strains and rotations. The structure of constitutive relations is derived for anisotropic elasto-plastic mono- and polycrystalline materials.