This study develops a framework for modeling deformation of individual pores in elastoviscoplastic earth material accounting for the effects of evolving pore size and shape on material hydraulic permeability. We describe the velocity field of a fluid within deforming pores of hypotrochoidal cross-sectional areas as a function of remote stress or deformation and elastoviscoplastic material properties using finite element analysis. We find that pore permeability decreases with increasing stress and deformation. Pore cross-sectional areas are mainly reduced in size while the shape remains constant. Under stress-controlled conditions, change in permeability depends on matrix constitutive laws and loading time while there is no such dependency for controlled strain. Permeability estimates based on the hydraulic radius, Saint-Venant, and Aissen approximations were in good agreement with numerical calculations for a deforming hypotrochoidal pore. We also show that permeability of a deforming hypotrochoidal pore can be modeled using a pore with equivalent elliptical cross-sectional area (equal initial permeability and size), providing the ellipse has the correct orientation. The study shows that fluid flow in deforming elastoviscoplastic earth material can be modeled on the pore scale knowing the evolution of pore size and shape employing rather simple relations between pore cross-sectional geometry and permeability.