We present a dynamical model of supernova feedback which follows the evolution of pressurized bubbles driven by supernovae in a multiphase interstellar medium (ISM). The bubbles are followed until the point of break-out into the halo, starting from an initial adiabatic phase to a radiative phase. We show that a key property which sets the fate of bubbles in the ISM is the gas surface density, through the work done by the expansion of bubbles and its role in setting the gas scaleheight. The multiphase description of the ISM is essential, and neglecting it leads to order-of-magnitude differences in the predicted outflow rates. We compare our predicted mass loading and outflow velocities to observations of local and high-redshift galaxies and find good agreement over a wide range of stellar masses and velocities. With the aim of analysing the dependence of the mass loading of the outflow, β (i.e. the ratio between the outflow and star formation rates), on galaxy properties, we embed our model in the galaxy formation simulation, GALFORM, set in the ∧ cold dark matter framework. We find that a dependence of β solely on the circular velocity, as is widely assumed in the literature, is actually a poor description of the outflow rate, as large variations with redshift and galaxy properties are obtained. Moreover, we find that below a circular velocity of ≈80 km s-1, the mass loading saturates. A more fundamental relation is that between β and the gas scaleheight of the disc, hg, and the gas fraction, fgas, as β ∝ hg 1.1 f gas 0.4 , or the gas surface density, Σg, and the gas fraction, as β ∝ Σg-0.6 fgas 0.8. We find that using the new mass loading model leads to a shallower faint-end slope in the predicted optical and near-IR galaxy luminosity functions. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.