AbstractMethods of solution for the nonlinear stress tensor field equations of matter in the creeping motion state are analysed. For homogeneous matter in two space dimensions the problem proves to be equivalent to the construction of symmetrical tensor fields of constant eigenvalue ratio (1− β)/(1+ β) and constant divergence g, where β and g are the internal friction parameter and the specific weight. A nonlinear second order differential equation remains if a modified Airy stress potential is introduced. This equation is solved generally for β21, g ≠ 0 and also for β2=1, g arbitrary. Physically, the corresponding stress fields describe weightless plastic matter and slowly moving anisotropic fluids respectively. For g ≠ 0 classes of new solutions are derived in th