Ray tracing is widely used to generate photorealistic images by tracing the paths of light rays through a scene and their interactions with scene objects. To accelerate ray tracing, an acceleration structure-typically a bounding volume hierar-chy-organizes scene primitives into an efficient spatial data structure, commonly traversed using a traversal stack. Modern GPUs are equipped with specialized ray tracing acceleration units to accelerate traversal and intersection tasks. With limited onchip storage, the traversal stack is kept short, leading to frequent spilling and reloading operations between on-chip buffers and offchip memory during stack overflows. This paper reveals that such overflows increase off-chip memory traffic, degrading overall performance. To address this, we propose SMS, a novel GPU architecture that leverages shared memory as a secondary traversal stack. The proposed design uses the shared memory stack to complement the primary on-chip stack, thus reducing off-chip traffic caused by stack overflows. Additionally, two optimizations for managing shared memory stacks are proposed: skewed bank access and dynamic intra-warp reallocation. Through effective management of traversal stacks, the proposed SMS architecture achieves a 23.2 % performance improvement over a baseline GPU that uses only a primary on-chip stack.