An upscaling approach for multi-porosity media is developed and demonstrated on a three-scale porous medium. The three-scale porous medium problem is analyzed using the so-called MultiSPH approach, which is a sequential SPH solver at multiple scales. By this approach, upscaling introduces drag forces on the SPH particles at coarser scales. The resulting permeabilities obtained by the MultiSPH approach are validated against available analytical solutions for simple microstructures. For complex microstructures, the MultiSPH approach is validated against detailed single-scale SPH simulations and experimental data. Sensitivities of fluid-structure interaction on the permeability is investigated.