In this paper, the problem of robust controller design for uncertain linear continuous- and discrete-time systems with circular pole constraints is considered. The problem we address is the design of robust state feedback controllers such that all poles of the closed-loop systems are placed within a prescribed circular region. Sufficient conditions for the existence of the desired controllers are given based on the generalized inverse theory. The analytical expression of the set of desired controllers is also presented. It is emphasized that, when the uncertainties are absent, the results include the characterization of all state-feedback controllers achieving the specified circular pole constraints. An illustrative example is given to show the applicability of the proposed design procedure.