  A pseudo-Riemannian manifold is introduced, with light-cone coordinates in
(4+1) dimensional space-time, to describe a Galilei covariant gravity. The
notion of 5-bein and torsion are developed and a galilean version of
teleparallelism is constructed in this manifold. The formalism is applied to
two spherically symmetric configurations. The first one is an ansatz which is
inferred by following the Schwarzschild solution in general relativity. The
second one is a solution of galilean covariant equations. In addition, this
Galilei teleparallel approach provides a prescription to couple the 5-bein
field to the galilean covariant Dirac field.
