In recent years, 3D Gaussian splatting (3DGS) has achieved remarkable progress in novel view synthesis. However, accurately reconstructing glossy surfaces under complex illumination remains challenging, particularly in scenes with strong specular reflections and multi-surface interreflections. To address this issue, we propose SSR-GS, a specular reflection modeling framework for glossy surface reconstruction. Specifically, we introduce a prefiltered Mip-Cubemap to model direct specular reflections efficiently, and propose an IndiASG module to capture indirect specular reflections. Furthermore, we design Visual Geometry Priors (VGP) that couple a reflection-aware visual prior via a reflection score (RS) to downweight the photometric loss contribution of reflection-dominated regions, with geometry priors derived from VGGT, including progressively decayed depth supervision and transformed normal constraints. Extensive experiments on both synthetic and real-world datasets demonstrate that SSR-GS achieves state-of-the-art performance in glossy surface reconstruction.