Many models of morphogenesis are forced to assume specific mechanical properties of cells, because the actual mechanical properties of living tissues are largely unknown. Here, we measure the rheology of epithelial cells in the cellularizing Drosophila embryo by injecting magnetic particles and studying their response to external actuation. We establish that, on timescales relevant to epithelial morphogenesis, the cytoplasm is predominantly viscous, whereas the cellular cortex is elastic. The timescale of elastic stress relaxation has a lower bound of 4 min, which is comparable to the time required for internalization of the ventral furrow during gastrulation. The cytoplasm was measured to be ∼10-fold as viscous as water. We show that elasticity depends on the actin cytoskeleton and conclude by discussing how these results relate to existing mechanical models of morphogenesis.