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We propose covert beamforming design frameworks for integrated radar sensing and communication (IRSC) systems, where the radar can covertly communicate with legitimate users under the cover of the probing waveforms without being detected by the eavesdropper. Specifically, by jointly designing the target detection beamformer and communication beamformer, we aim to maximize the radar detection mutual information (MI) (or the communication rate) subject to the covert constraint, the communication rate constraint (or the radar detection MI constraint), and the total power constraint. For the perfect eavesdropper's channel state information (CSI) scenario, we transform the covert beamforming design problems into a series of convex subproblems, by exploiting semidefinite relaxation, which can be solved via the bisection search method. Considering the high complexity of iterative optimization, we further propose a single-iterative covert beamformer design scheme based on the zero-forcing criterion. For the imperfect eavesdropper's CSI scenario, we develop a relaxation and restriction method to tackle the robust covert beamforming design problems. Simulation results demonstrate the effectiveness of the proposed covert beamforming schemes for perfect and imperfect CSI scenarios.