Understanding human development is of fundamental biological and clinical importance. Despite its significance, mechanisms behind human embryogenesis remain largely unknown. Here, we attempt to model human early embryo development with expanded pluripotent stem cells (EPSCs) in 3-dimensions. We define a protocol that allows us to generate self-organizing cystic structures from human EPSCs that display some hallmarks of human early embryogenesis. These structures mimic polarization and cavitation characteristic of pre-implantation development leading to blastocyst morphology formation and the transition to post-implantation-like organization upon extended culture. Single-cell RNA sequencing of these structures reveals subsets of cells bearing some resemblance to epiblast, hypoblast and trophectoderm lineages. Nevertheless, significant divergences from natural blastocysts persist in some key markers, and signalling pathways point towards ways in which morphology and transcriptional-level cell identities may diverge in stem cell models of the embryo. Thus, this stem cell platform provides insights into the design of stem cell models of embryogenesis.