  We discuss the recent proposal of implementing Doubly Special Relativity in
configuration space by means of Finsler geometry. Although this formalism leads
to a consistent description of the dynamics of a particle, it does not seem to
give a complete description of the physics. In particular, the Finsler line
element is not invariant under the deformed Lorentz transformations of Doubly
Special Relativity. We study in detail some simple applications of the
formalism.
