A novel multicast communication system with movable antennas (MAs) is proposed, where the antenna position optimization is exploited to enhance the transmission rate. Specifically, an MA-assisted two-user multicast multiple-input single-input system is considered. The joint optimization of the transmit beamforming vector and transmit MA positions is studied by modeling the motion of the MA elements as discrete movements. A low-complexity greedy search-based algorithm is proposed to tackle this non-convex inter-programming problem. A branch-and-bound (BAB)-based method is proposed to achieve the optimal multicast rate with a reduced time complexity than the brute-force search by assuming the two users suffer similar line-of-sight path losses. Numerical results reveal that the proposed MA systems significantly improve the multicast rate compared to conventional fixed-position antennas (FPAs)-based systems.