Cytokinesis, the fission of a mother cell into two daughter cells, is a simple and dramatic cell shape change. Here, we examine the dynamics of cytokinesis by using a combination of microscopy, dynamic measurements, and genetic analysis. We find that cytokinesis proceeds through a single sequence of shape changes, but the kinetics of the transformation from one shape to another differs dramatically between strains. We interpret the measurements in a simple and quantitative manner by using a previously uncharacterized analytic model. From the analysis, wild-type cytokinesis appears to proceed through an active, extremely regulated process in which globally distributed proteins generate resistive forces that slow the rate of furrow ingression. Finally, we propose that, in addition to myosin II, a Laplace pressure, resulting from material properties and the geometry of the dividing cell, generates force to help drive furrow ingression late in cytokinesis.