Animal cells dividing in culture undergo a dramatic sequence of morphological changes, characterized by cytoskeletal disassembly as cells round up, redistribution of actin, myosins and other cytoplasmic and surface molecules into the cleavage furrow(1-11), and respreading(12), before daughter cells finally separate at the mid-body(13). Knowledge of forces governing these movements is critical to understanding their mechanisms, including whether formation of the cleavage furrow results from increased force generation at the equator(14,15) or relaxation at the poles(16), and whether traction force subsequently mediates cytofission of the intercellular bridge(5,13,17,18). We have quantitatively mapped traction forces in dividing cells, by extending the silicone-rubber substratum method(19) to detect forces of nanonewtons to micro-newtons. We used a new silicone polymer to fabricate substrata whose compliance can be adjusted precisely by ultraviolet irradiation. We show that traction force appears locally at the furrow in the absence of relaxation at the poles during cleavage. Force also rises as connected daughter cells respread and attempt to separate, suggesting that tension contributes to the severing of the intercellular bridge when cytokinesis is completed.