This paper addresses the problem of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) among users in a multicast communication system enhanced by moveable antennas (MA). The system consists of a base station (BS) equipped with multiple transmit MAs and multiple single-MA users grouped into multiple multicast groups. The authors propose an efficient alternating optimization (AO) algorithm to jointly optimize the positions of transmit and receive MAs and the transmit beamforming. The algorithm is designed to handle the non-convex optimization problem by using successive convex approximation (SCA) techniques, particularly focusing on constructing concave lower bounds for the signal-to-noise ratio (SNR) of each user. The proposed algorithm is first validated in a single-group scenario and then extended to the general multi-group case. Simulation results demonstrate that the proposed algorithm converges faster than existing methods and achieves a 3.4% improvement in max-min SINR. Additionally, it significantly enhances max-min SNR/SINR compared to benchmarks using only receive MAs, only transmit MAs, or both transmit and receive FPAs.This paper addresses the problem of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) among users in a multicast communication system enhanced by moveable antennas (MA). The system consists of a base station (BS) equipped with multiple transmit MAs and multiple single-MA users grouped into multiple multicast groups. The authors propose an efficient alternating optimization (AO) algorithm to jointly optimize the positions of transmit and receive MAs and the transmit beamforming. The algorithm is designed to handle the non-convex optimization problem by using successive convex approximation (SCA) techniques, particularly focusing on constructing concave lower bounds for the signal-to-noise ratio (SNR) of each user. The proposed algorithm is first validated in a single-group scenario and then extended to the general multi-group case. Simulation results demonstrate that the proposed algorithm converges faster than existing methods and achieves a 3.4% improvement in max-min SINR. Additionally, it significantly enhances max-min SNR/SINR compared to benchmarks using only receive MAs, only transmit MAs, or both transmit and receive FPAs.