In this article, we develop an analytical radiation-pattern model for pinching-antenna systems (PASS) based on a two-dimensional dielectric slab waveguide. The model is derived in two steps. First, we employ coupled-mode theory (CMT) to derive a closed-form expression for the field coupled into the pinching antennas (PAs). Second, we use this analytical field profile as a scattering source model and derive the far-field radiation pattern via a two-dimensional radiation integral. We validate the proposed model against full-wave finite-element simulations performed in COMSOL Multiphysics, showing that it accurately reproduces the directional radiation characteristics of PASS. In contrast, most existing works model PAs as omni-directional point radiators, which simplifies system-level analysis but does not accurately capture the underlying electromagnetic radiation mechanism. Because the proposed model is given in closed form, it can be easily integrated into existing system-level PASS models to replace the assumed omni-directional pattern with a physically motivated directional radiation pattern. Finally, numerical simulations quantify the performance degradation that arises when the directional behavior of PAs is neglected in a representative wireless communications scenario.