The flow of non-Newtonian fluids through evolving porous media is involved in important processes including blood flow and remediation of deformable aquifers. However, the effects of a moving solid boundary and the coupling between fluid rheology and solid deformation are still unclear. This study considers the steady and oscillatory flows of a yield stress fluid through a bundle of deformable channels. Simple semi-empirical expressions to predict the relationships between Darcy velocity and pressure gradient as a function of pore sizes, shear-rheology parameters and inlet pressure are developed, based on the results of innovative numerical simulations. The results show that channel deformation reduces the minimum pressure gradient required to induce the flow of a yield stress fluid through a porous medium, which results in lower values of Darcy-scale viscosity. For the considered conditions, macroscopic flow can be accurately predicted without a detailed knowledge of the hydraulic conductances of the deformed pores.