Abstract - Thanks to their softness, biocompatibility, porosity and ready availability, hydrogels are commonly used in microfluidic assays and organ-on-chip devices as a matrix for cells. They not only provide a supporting scaffold for the differentiating cells and the developing organoids, but also serve as the medium for transmitting oxygen, nutrients, various chemical factors, and mechanical stimuli to the cells. From a bioengineering viewpoint, the transmission of forces from fluid perfusion to the cells through the hydrogel is critical to the proper function and development of the cell colony. In this paper, we develop a poroelastic model to represent the fluid flow through a hydrogel containing a biological cell modeled as a hyperelastic inclusion. In geometries representing shear and normal flows that occur frequently in microfluidic experiments, we examine how the perfusion engenders interstitial flow in the gels and displaces and deforms the embedded cell. This provides a computational tool to design the geometry and flow conditions to achieve optimal flow and stress fields inside the hydrogels and around the cell.