The UV escape fraction, f esc UV, is a key parameter determining the apparent SED of star forming galaxies. However, it is not well known how f esc UV depends on the global geometry of dust distribution, nor how it evolves with time, although several models are proposed (e.g., Calzetti (2001)). We use ~130 normal star-forming galaxies (114 at z ~ 0 from Cortese et al. (2012) and 15 at z ~ 1–3 from Magnelli et al. (2012) and Saintonge et al. (2013)), to find that the z ~ 0 galaxies show a relatively tight anti-correlation between f esc UV and surface dust mass density, Σd (See Fig. 1(a)). This correlation can be reproduced by a dust geometry model that well-mixed stars and dust follow the same exponential profile (Fig. 1(b)) with an effective mass-absorption coefficient κ(1600 Å) = 7.6+5.3 −3.0 × 104 cm2 g−1, similar to the Milky Way value including absorption and scatter. The z ~ 1–3 galaxies are not inconsistent with this model. Our model can be easily implemented in semi-analytic models and cosmological hydrodynamics simulations (CHSs) of galaxy formation. Initial results for Shimizu et al. (2014)'s CHSs are presented.