Interstitial fluid flow has been shown to affect the organization and behavior of cells in 3D environments in vivo and in vitro, yet the forces driving such responses are not clear. Due to the complex architecture of the extracellular matrix (ECM) and the difficulty of measuring fluid flow near cells embedded in it, the levels of shear stress experienced by cells in this environment are typically estimated using bulk-averaged matrix parameters such as hydraulic permeability. While this is useful for estimating average stresses, it cannot yield insight into how local matrix fiber architecture-which is cell-controlled in the immediate pericellular environment-affects the local stresses imposed on the cell surface. To address this, we used computational fluid dynamics to study flow through an idealized mesh constructed of a cubic lattice of fibers simulating a typical in vitro collagen gel. We found that, in such high porosity matrices, the fibers strongly affect the flow fields near the cell, with peak shear stresses up to five times higher than those predicted by the Brinkman equation. We also found that minor remodeling of the fibers near the cell surface had major effects on the shear stress profile on the cell. These findings demonstrate the importance of fiber architecture to the fluid forces on a cell embedded in a 3D matrix, and also show how small modifications in the local ECM can lead to large changes in the mechanical environment of the cell.