A novel concept of waveguide division multiple access (WDMA) is proposed for multi-user pinching-antenna systems (PASS). The key principle of WDMA is to allocate each user with a dedicated waveguide, which is regarded as a new type of radio resources, so as to facilitate multi-user communications. By adjusting the activation positions of pinching antennas (PAs) over each waveguide, the pinching beamforming can be exploited for intended user signal enhancement and inter-user interference mitigation. Considering both ideal continuous and practical discrete PA position activation schemes, a joint power allocation and pinching beamforming optimization problem is formulated for the maximization of the sum rate. An alternating optimization-based algorithm is developed to address the formulated nonconvex problem. For solving the power allocation subproblem, the successive convex approximation method is invoked. For the pinching beamforming design subproblem, a penalty-based gradient ascent algorithm is first developed for the continuous PA activation case. Then, for the discrete PA activation case, a matching theory-based algorithm is proposed to achieve the near-optimal performance but with a low complexity. Numerical results unveil that: 1) For both continuous and discrete activation cases, PASS can achieve a significant performance gain over conventional fixed-position antenna systems; 2) the proposed WDMA can effectively underpin multi-user communications with the near orthogonality in free space achieved by the pinching beamforming; and 3) the performance gap between the discrete and continuous activation cases can be significantly alleviated with practically feasible numbers of PA candidate positions.