With every beat of the heart, inflation of the lung or peristalsis of the gut, cell types of diverse function are subjected to substantial stretch. Stretch is a potent stimulus for growth, differentiation, migration, remodelling and gene expression. Here, we report that in response to transient stretch the cytoskeleton fluidizes in such a way as to define a universal response class. This finding implicates mechanisms mediated not only by specific signalling intermediates, as is usually assumed, but also by non-specific actions of a slowly evolving network of physical forces. These results support the idea that the cell interior is at once a crowded chemical space and a fragile soft material in which the effects of biochemistry, molecular crowding and physical forces are complex and inseparable, yet conspire nonetheless to yield remarkably simple phenomenological laws. These laws seem to be both universal and primitive, and thus comprise a striking intersection between the worlds of cell biology and soft matter physics.