In this paper the secondary creep stage of anisotropic solids in a state of multiaxial stress is considered. The theory is based on the assumption of the existence of a creep potential, which can depend only on invariants of the stress tensor or its deviator, if the material is isotropic. The anisotropic behavior is described by using a mapped stress tensor instead of the actual stress tensor in the isotropic creep potential. Assuming a linear transformation, the anisotropic behavior is expressed by a material tensor of rank four. The theory of the creep potential is based upon the principle of maximum dissipation rate, from which, following Lagrange's method in connection with a creep condition, one obtains the flow rule of anisotropic materials. This flow rule leads to the constitutive equations formulated in this paper. The material constants involved in these equations are related to experimental data. For example, the orthotropic case is considered, and the Poynting‐effect is accounted for. Furthermore, the influence of the “second‐order” effect and of the anisotropy on the creep‐behavior of a thin‐walled tube subjected to internal pressure is investigated.