This paper proposes a movable waveguide (MW)-enabled pinching-antenna system (PASS), in which each waveguide is connected via a flexible cable and can be linearly moved by drivers. By simultaneously moving the MWs and the pinching antennas (PAs) on them, MW-enabled PASS can effectively track user locations and form flexible array geometries for efficient beamforming. We first examine the special case with a single user and derive the closed-form solutions for the optimal MW positions as well as an upper bound on the user rate. Furthermore, we develop a two-step optimization algorithm to maximize the achievable rate for the user, where the first step determines the optimal MW positions using the derived closed-form solutions, and the second step alternately optimizes the PA positions through a one-dimensional (1D) local search based on the user location. Then, for the general multi-user scenario, we derive the upper bounds on the minimum rate among all users. To maximize their minimum rate, we propose a low-complexity two-scale optimization algorithm, where the large-scale global search coarsely determines the MW and PA positions, followed by a small-scale local search to finely tune them. In addition, a two-timescale optimization scheme based on statistical channel information is investigated to reduce the mechanical movement overhead of the MWs. Simulation results demonstrate that the proposed scheme achieves performance close to the derived bounds. It also flexibly adapts to different user distributions compared with the conventional PASS employing dense or sparse fixed-position waveguides (FPWs), as well as fixed-position antenna (FPA) schemes.

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