Soil arching is a classic well-known phenomenon in soil mechanics, commonly found induced by underground excavations, tunnel excavations, and retaining structures, etc. This phenomenon has been studied for decades through the trapdoor problem, either theoretically, experimentally or numerically. Recent studies have focused on laboratory experiments or theoretical investigations to explore the soil arching effect, including stress redistribution, deformation patterns, and failure mechanisms. However, there is still a limited understanding of the nonlinear soil stress-strain response in large deformation schemes close to material failure. Additionally, the current scale of the experiment is not comparable to a real-world scenario. In this study, we aim to simulate a two-dimensional trapdoor problem using the material point method (MPM). We first validated the numerical model via available laboratory experiments from the literature. The capability and limitation of the two-dimensional, MPM simulation were discussed and also compared with the finite element simulation. In general, the MPM code effectively simulated the soil arching behavior by varying the soil model height or displacement of the trapdoor openings. Subsequently, a series of numerical simulations were performed to explore the impact of dry sand's relative density on soil arching behavior in terms of shear zone distribution and possible failure mechanism. Overall, to better understand the capability and limitation of MPM code in large deformation modeling, this study utilized the MPM code to simulate the two-dimensional trapdoor problem, validating the model against existing laboratory experiments and investigating the influence of dry sand's relative density on soil arching behavior.