Laminar flows through porous media represent a crucial problem in many fields of engi- neering. In the present work, we aim to study the breakup of solid porous media with brittle mechanical properties due to the action of fluid dynamics forces exerted by a lam- inar duct flow. The problem is addressed in the framework of the 3D incompressible Navier-Stokes equations coupled with peridynamics via Immersed Boundary Method. The three-dimensional domain consists of a rectangular prism with wall boundary condi- tions applied to the lateral, lower and upper surfaces. A 2D Poiseuille inflow is applied at the inlet, whereas a convective outflow at the outlet. The domain is discretized by using Nx x Ny x Nz = 128 x 64 x 64 nodes along the flow and wall-normal directions, respectively. Each of the considered porous media relies on a set of 53067 Lagrangian nodes. The medium is obtained by subtracting from a rectangular box of solid material a given number of randomly distributed spheres, Ns, of fixed radius rs to obtain a desired poros- ity. We will present the results of different simulations and several statistics concerning the stress and strain distribution within the porous material before and after breakup. Different geometrical configurations will be considered in terms of the pore radius and porosity. Moreover, the reliability of different fracture criteria will be analyzed.