This paper investigates flexible beamforming in an integrated sensing and communication (ISAC) network with movable antennas (MAs). The system integrates a bistatic radar system into a multi-user multiple-input-single-output (MU-MISO) system, enabling array response reconfiguration by adjusting antenna positions. The proposed flexible beamforming aims to maximize the sum of communication rate and sensing mutual information (MI) through joint optimization of the beamforming matrix and antenna positions. The fractional programming (FP) method is used to transform the non-convex objective function, and an alternating optimization (AO) algorithm is proposed to update the beamforming matrix and antenna positions. Karush–Kuhn–Tucker (KKT) conditions are employed to derive the closed-form solution for the beamforming matrix, while a search-based projected gradient ascent (SPGA) method is used to update the antenna positions. Simulation results demonstrate that MAs significantly enhance ISAC performance, achieving a 59.8% improvement over fixed uniform arrays. The proposed algorithm outperforms both fixed antenna configurations and the direct gradient ascent (DGA) method, especially in high signal-to-noise ratio (SNR) conditions and large feasible antenna regions.This paper investigates flexible beamforming in an integrated sensing and communication (ISAC) network with movable antennas (MAs). The system integrates a bistatic radar system into a multi-user multiple-input-single-output (MU-MISO) system, enabling array response reconfiguration by adjusting antenna positions. The proposed flexible beamforming aims to maximize the sum of communication rate and sensing mutual information (MI) through joint optimization of the beamforming matrix and antenna positions. The fractional programming (FP) method is used to transform the non-convex objective function, and an alternating optimization (AO) algorithm is proposed to update the beamforming matrix and antenna positions. Karush–Kuhn–Tucker (KKT) conditions are employed to derive the closed-form solution for the beamforming matrix, while a search-based projected gradient ascent (SPGA) method is used to update the antenna positions. Simulation results demonstrate that MAs significantly enhance ISAC performance, achieving a 59.8% improvement over fixed uniform arrays. The proposed algorithm outperforms both fixed antenna configurations and the direct gradient ascent (DGA) method, especially in high signal-to-noise ratio (SNR) conditions and large feasible antenna regions.