  The notions of bienergy of a smooth mapping and of biharmonic map between
Riemannian manifolds are extended to the case when the domain is Finslerian. We
determine the first and the second variation of the bienergy functional, the
equations of Finsler-to-Riemann biharmonic maps and some specific examples. Two
notable results in Riemannian geometry concerning the inexistence of
nonharmonic biharmonic maps are extended without difficulty in our case.
