  We consider Finsler submanifolds $M^n$ of nonnegative Ricci curvature in a
Minkowski space $\mathbb{M}^{n+p}$ which contain a line or whose relative
nullity index is positive. For hypersurfaces, submanifolds of codimension two
or of dimension two, we prove that the submanifold is a cylinder, under a
certain condition on the inertia of the pencil of the second fundamental forms.
We give an example of a surface of positive flag curvature in a
three-dimensional Minkowski space which is not locally convex.
