An analysis has been carried out to determine the thermodynamic requirements for homogeneous nucleation of a vapor bubble when the pressure drops inside a constant-volume container of liquid. This situation can occur in phase change processes when a rigid vessel filled with liquid is cooled. The nucleation equations at constant volume have a somewhat different character from their more familiar constant-pressure counterparts that reflects the change in the boundary conditions for bubble formation. Both the physical and mathematical implications of the new solution are explored in detail, and it is shown to reduce to the well known constant-pressure result in the limiting case of avery large container volume. To illustrate an application of the new equations. some numerical examples have been worked out for homogeneous nucleation of water with various container sizes and initial liquid temperatures. In addition to increasing fundamental understanding of homogeneous nucleation, these results should prove valuable for calculation purposes when vapor nucleation takes place under isochoric rather than isobaric conditions.