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Correlated supernovae from an OB association create a superbubble: a large, thin, shell of cold gas surrounding a hot pressurized interior. Because supernova blast waves usually become subsonic before reaching the walls of the shell or cooling radiatively, we may reasonably approximate the energy input from supernovae as a continuous luminosity. Using the Kompaneets (thin-shell) approximation, we numerically model the growth of superbubbles in various stratified atmospheres. A dimensionless quantity predicts whether a superbubble will blow out of the H I disk of a spiral galaxy (and begin to accelerate upward) or collapse. Superbubbles blow out of the H I layer when they have a radius in the plane between one and two scale heights. They blow out only one side of a disk galaxy if their centers are more than 50-60 pc above the plane and the gas layer has density and scale height typical of the Milky Way. Fingers of warm interstellar gas intrude into the hot interior when the superbubble overtakes dense clouds.