Lumenogenesis within the epiblast represents a critical step in early human development, priming the embryo for future specification and patterning events. However, little is known about the specific mechanisms that drive this process due to the inability to study the early embryo in vivo. While human pluripotent stem cell (hPSC)-based models recapitulate many aspects of the human epiblast, most approaches for generating these 3D structures rely on ill-defined, reconstituted basement membrane matrices. Here, we designed synthetic, nonadhesive polyethylene glycol (PEG) hydrogel matrices to better understand the role of matrix mechanical cues in iPSC morphogenesis, specifically elastic modulus. First, we identified a narrow range of hydrogel moduli that were conducive to the hPSC viability, pluripotency, and differentiation. We then used this platform to investigate the effects of the hydrogel modulus on lumenogenesis, finding that matrices of intermediate stiffness yielded the most epiblast-like aggregates. Conversely, stiffer matrices impeded lumen formation and apico-basal polarization, while the softest matrices yielded polarized but aberrant structures. Our approach offers a simple, modular platform for modeling the human epiblast and investigating the role of matrix cues in its morphogenesis.