Implantation triggers critical morphological transformations in the embryo, where the epiblast transitions from a cluster of unpolarized cells into a highly organized, polarized epithelium characterized by a central lumen. Human pluripotent stem cells (hPSCs) are valuable models for studying this process, but conventional matrices like Matrigel have significant limitations, including variability and poor control over mechanical properties. To overcome these challenges, we developed a synthetic polyethylene glycol (PEG) hydrogel system with tunable mechanical stiffness to model peri-implantation epiblast morphogenesis. Our platform enables hPSCs to form unpolarized 3D aggregates that undergo stiffness-dependent transformation into lumen-forming, apicobasal-polarized structures resembling epiblast morphogenesis during peri-implantation. Unlike natural ECMs, PEG hydrogels maintain hPSC pluripotency for extended periods and support trilineage differentiation upon induction. The modular hydrogel design facilitates targeted mechanistic studies on the biophysical and biochemical regulation of cell morphogenesis. We present a comprehensive protocol for fabricating PEG hydrogels, encapsulating hPSCs, and assessing cell polarity, lumen formation, and pluripotency using immunostaining and RT-PCR. This platform provides a robust, cost-effective, and versatile tool for advancing developmental biology and regenerative medicine.