Movable antennas (MAs) can reshape the propagation environment by continuously adjusting their spatial positions compared with fixed-position antennas (FPAs). Leveraging this advantage, we develop an alternating optimization framework for covert integrated sensing and communication (ISAC) systems. This framework jointly optimizes the MA placements and beamforming designs. The goal is to maximize a weighted combination of the communication rate and the sensing mutual information. Key constraints confine the MAs to predefined two-dimensional regions, and impose a covertness requirement to minimize the probability of detection by an untrusted warden. This optimization problem is non-convex in nature. Hence, the proposed method decomposes it into two subproblems and solve them iteratively. The beamforming vectors are optimized by leveraging semidefinite relaxation and successive convex approximation, with the MA positions held fixed. Afterward, the beamforming vectors are fixed, and the MA positions are refined using surrogate trigonometric functions. The solution converges in a monotonic manner, yielding a high-quality suboptimal solution of the system. Numerous simulations show the proposed scheme achieves substantial improvements over FPA benchmarks. Specifically, the weighted sum rate improves with the number of MA elements, and mobility regions of only a few wavelengths can considerably improve covert ISAC performance.
