Recent experiments and molecular dynamics simulations have proven that polymer chains are less confined in layers near the free surfaces of submicron-nanosized pores. A recent model has incorporated this observed variable chain confinement at void surfaces in a mechanism-based hyperelastic model. This work employs that model to do two things: explain the large discrepancy between classical homogenization theories and physical experiments measuring the modulus of nanoporous polymers, and describe the instability behavior (onset and postinstability deformation) of this class of materials. The analysis demonstrates that less confinement of polymer chains near free surfaces of voids inhibits tilting buckling while promoting pattern transformation. The sensitivity of geometric instability modes to void size is also studied in depth, helping lay the foundation for fabricating solids with tunable acoustic and optical properties. The simulation approach outlined provides experimentalists with a practical route to estimate the thickness of the interfacial layer in nanoporous polymers.