This article presents an innovative approach to model particle bed growth through suspension dead-end filtration, a process of paramount importance in various industrial and environmental contexts. More precisely, it focuses on the numerical formulation of a continuous approach based on a Stokes–Darcy coupling. In a Level-Set/FEM frame, this model effectively captures the dynamic evolution of particle beds (cake), taking into account the interaction between suspended particles and porous media. Model validation is also a key focus of this paper. Numerical tests are carried out under various conditions, their results are compared with analytical solutions and experimental data drawn from the literature. This permits to corroborate the predictive capabilities of the model, confirming the robustness and accuracy of the proposed approach. Firstly, Stokes–Darcy coupled flows are investigated in simplified cases such as rectangular geometries and coaxial cylinders. These scenarios serve as benchmarks to assess the model performance under simple and varied conditions. Additionally, the more challenging case of a three-dimensional anisotropic flow between two ellipsoids is addressed, where the evolution of the cake takes place in three dimensions. Through rigorous analysis and comparison with analytical solutions, the model is proved efficient in capturing the inherent complexities of such scenarios. Finally, richer two-dimensional Stokes–Darcy flows are considered, in the presence of both impermeable and permeable obstacles, representing a crucial step towards modelling real industrial processes. This last study highlights not only the formation of particle-free zones but also the practical relevance of this work.