  We establish the existence and uniqueness of the transonic shock solution for
steady isentropic Euler system with an external force in a rectangular cylinder
under the three-dimensional perturbations for the incoming supersonic flow, the
exit pressure and the external force. The external force has a stabilization
effect on the transonic shocks in flat nozzles and the transonic shock is
completely free, we do not require it passing through a fixed point. By
utilizing the deformation-curl decomposition to decouple the hyperbolic and
elliptic modes in the steady Euler system effectively and reformulating the
Rankine-Hugoniot conditions, the transonic shock problem is reduced to a
deformation-curl first order system for the velocity field with nonlocal terms
supplementing with an unusual second order differential boundary condition on
the shock front, an algebraic equation for determining the shock front and two
transport equations for the Bernoulli's quantity and the first component of the
vorticity.
