Cavitation rheology is a recently developed measurement method for studying the mechanical properties of polymer gels from sub-micron to millimeter length scales at arbitrary locations within the network material. Current knowledge has focused on understanding the relationship between materials properties, such as modulus or fracture strength, and the maximum pressure for initiating cavitation. After the maximum pressure is reached, the growth of the bubble and the associated pressure drop is sudden and uncontrolled. We develop methods to control the growth of the bubble and to understand the relationship between cavity growth, pressure drop, and the material properties of the surrounding polymer network. We conduct these measurements on swollen networks of a triblock copolymer of poly(methyl methacrylate)–poly(n-butyl acrylate)–poly(methyl methacrylate) (PMMA–PnBA–PMMA)