<p>Dynamic high-fidelity simulation in fields such as metal forming and geotechnical engineering remains challenged by mesh distortion and inadequate stress resolution. This study proposes the hybrid stress material point method (HS-MPM), a novel dual-mesh hybrid framework that synergistically couples the material point method (MPM) and the hybrid stress finite element method (HS-FEM) to concurrently harness the distortion resistance of MPM and the high-fidelity stress accuracy of HS-FEM. The framework employs arbitrary polygonal elements for spatial discretization to enhance geometric adaptability. Its core innovation lies in a dual strategy: (1) a Lagrangian physical mesh based on HS-FEM directly constructs high-resolution stress fields through independently assumed self-equilibrating stress fields; while (2) a recyclable Eulerian background grid solves the momentum equations explicitly, thereby inherently avoiding mesh distortion. Numerical benchmark tests demonstrate that the proposed method exhibits strong computational robustness and achieves outstanding stress resolution capability. Notably, it attains accuracy comparable to refined traditional FEM models using significantly fewer elements. The framework thus provides an efficient and precise numerical tool for transient dynamic analysis involving large rotation, finite strains, and stress concentrations.</p>