The string model is applied to networks of magnetic flux lines in a strongly anisotropic superconducting medium. The notion of vectorial anisotropic string tension is introduced. It is shown that, contrary to the case of isotropic string, the tension is not tangent to the flux line. The equilibrium configurations of flux lines pinned to the anisotropic material are examined. The existence of spontaneously bent extremals, energetically more favorable than straight lines, is proven. The question of degeneracy of the solutions is discussed.
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