An experimental and numerical investigation of the effect of material anisotropy on the self-positioning of epitaxial nanostructures has been performed. The self-positioning occurs due to a lattice mismatch between two epitaxial material layers (GaAs and In0.2Ga0.8As) of a hinge. Both materials have cubic crystal symmetry and possess anisotropic mechanical properties. The dependence of the hinge curvature radius on the material orientation angle was obtained experimentally by creating self-positioning hinges with different angles between the hinge axis and material crystallographic axes. The same self-positioning structures were modelled by solving geometrically nonlinear problems with the help of the finite element method. Experimental and numerical values of the hinge curvature radius are in qualitative agreement. It is found that material anisotropy significantly affects the shape of self-positioning structures.