<p>This study proposes a novel gravity-considered three-dimensional arbitrary polyhedral hybrid stress finite element method (abbreviated as G-3DPHSEM) for numerical simulation of three-dimensional problems considering gravity effects. Based on the hybrid stress finite element theory, this study integrates gravity terms into the modified complementary energy functional of hybrid stress finite element, and proposes the functional of G-3DPHSEM. To verify the effectiveness of the method, a single-material model example, a multi-material model example, and a complex model example were constructed for numerical simulation. The calculation results of G-3DPHSEM were compared with those of the commercial finite element software. The comparison results show that: for the single-material case, the errors of this method are generally below 3% compared with commercial software’s results; for the multi-material case, the errors are generally below 5% compared with commercial software’s results; for the complex model, the errors are generally below 10% compared with commercial software’s results. Meanwhile, this method also demonstrates significant advantages in mesh generation: while ensuring computational accuracy, it possesses the core advantages of flexible mesh generation and substantial reduction in the number of elements, providing new ideas for numerical simulation of complex gravity problems (such as large and complex slopes and other engineering problems).</p>