This paper focuses on the reduction of radar cross section (RCS) for a cavity embedded in an infinite ground plane. By introducing a transparent boundary condition, the unbounded scattering problem is reduced to a bounded domain problem. RCS reduction for the cavity is formulated as a shape optimization problem involving the Helmholtz equation. The existence of the minimizer is proved under an appropriate constraint. Descent directions of the objective function with respect to the boundary may be found via the domain derivative. It is used in a gradient-based optimization scheme to find the optimal shape of the cavity. Numerical examples show that the RCS is effectively reduced at different incident frequencies.