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The radar cross section (RCS) of a flat plate covered with a cold collisional inhomogeneous plasma has been studied using a 3-D finite-difference time-domain (FDTD) method for electromagnetics. Two problems have been considered. In problem 1, using experimentally reported plasma density profiles, we have observed some interesting features in the bistatic RCS and provided simple physical interpretations for some of these features. The simulations confirm that a plasma shroud can successfully be used for reducing the RCS of a flat plate at almost all scattering angles, although the RCS could increase at some other angles. This is a novel extension of the FDTD method for the calculation of the bistatic RCS of an object shielded by a nonuniform collisional plasma. Problem 2 involves an optimization study for the input power required to achieve a desired RCS reduction (RCSR), examining a variety of plasma density levels and spatial profiles. For this optimization study, we have considered a helium plasma produced by a high-energy electron beam. We find that the maximum achievable reduction increases monotonically with power up to an optimum point, beyond which the RCSR decreases, finally showing some tendency to saturate. This is of practical importance and indicates the usefulness of FDTD simulations in identifying the optimal point. Furthermore, at a given power level, there can be a considerable scatter in the RCSR achievable. This is because various combinations of the plasma parameters, differing considerably in their RCSR abilities, could require the same power to sustain them. Simulations would be of great use in helping to identify the best profiles to be used for a given input power level.