Recently, the pinching-antenna system (PASS) has emerged as a promising architecture owing to its ability to reconfigure large-scale path loss and signal phase by activating radiation points along a dielectric waveguide. However, existing studies mainly focus on line-shaped PASS architectures, whose limited spatial flexibility constrains their applicability in multiuser and indoor scenarios. In this paper, we propose a novel two-dimensional (2D) pinching-antenna system (2D-PASS) that extends the conventional line-shaped structure into a continuous dielectric waveguide plane, thereby forming a reconfigurable radiating plane capable of dynamic beam adaptation across a 2D spatial domain. An optimization framework is developed to maximize the minimum received signal-to-noise ratio (SNR) among user equipments (UEs) by adaptively adjusting the spatial configuration of pinching antennas (PAs), serving as an analog beamforming mechanism for dynamic spatial control. For the continuous-position scenario, a particle swarm optimization (PSO)-based algorithm is proposed to efficiently explore the nonconvex search space, while a discrete variant is introduced to accommodate practical hardware constraints with limited PA placement resolution. Simulation results demonstrate that the proposed 2D-PASS substantially improves the minimum SNR compared with conventional line-shaped PASS and fixed-position antenna (FPA) benchmarks, while maintaining robustness under varying user distributions and distances.