A coupled dual porosity Stokes model has been proposed in recent years to help modeling fractured porous media with large conduits. A numerical solution of such a model that works in both 2D and 3D in parallel has been implemented using FEniCS. In this talk, we describe tests for the convergence of this implementation with sample problems in both 2D and 3D, describe the performance and scalability of this implementation thoroughly, and compare the performance between different solvers and preconditioners.