The flow of viscoplastic materials through staggered arrays of tubes is analyzed. The mechanical behavior of the materials is assumed to obey the generalized Newtonian liquid (GNL) model, with a viscosity function given by the biviscosity law. The governing equations of this flow are solved numerically using a finite-volume method with a non-orthogonal mesh. For a representative range of the relevant parameters, results are presented in the form of velocity, pressure and viscosity fields. The pressure drop is also given as a function of rheological and geometric parameters.