  We construct the T duals of certain type IIA brane configurations with one
compact dimension (elliptic models) which contain orientifold planes. These
configurations realize four-dimensional $\NN=2$ finite field theories. For
elliptic models with two negatively charged orientifold six-planes, the T duals
are given by D3 branes at singularities in the presence of O7-planes and
D7-branes. For elliptic models with two oppositely charged orientifold planes,
the T duals are D3 branes at a different kind of orientifold singularities,
which do not require D7 branes. We construct the adequate orientifold groups,
and show that the cancellation of twisted tadpoles is equivalent to the
finiteness of the corresponding field theory. One family of models contains
orthogonal and symplectic gauge factors at the same time. These new
orientifolds can also be used to define some six-dimensional RG fixed points
which have been discussed from the type IIA brane configuration perspective.
