  This paper is devoted to the structural stability of a transonic shock
passing through a flat nozzle for two-dimensional steady compressible flows
with an external force. We first establish the existence and uniqueness of one
dimensional transonic shock solutions to the steady Euler system with an
external force by prescribing suitable pressure at the exit of the nozzle when
the upstream flow is a uniform supersonic flow. It is shown that the external
force helps to stabilize the transonic shock in flat nozzles and the shock
position is uniquely determined. Then we are concerned with the structural
stability of these transonic shoc solutions when the exit pressure is suitably
perturbed. One of the new ingredients in our analysis is to use the
deformation-curl decomposition to the steady Euler system developed in
\cite{WengX2019} to deal with the transonic shock problem.
