The location and shape of a planetary magnetopause is principally determined by the dynamic pressure, Dp, of the solar wind, the orientation of the planet's magnetic dipole with respect to the solar wind flow, and by the distribution of stresses inside the magnetosphere. The magnetospheres of Saturn and Jupiter have strong internal plasma sources compared to the solar wind source and also rotate rapidly, causing an equatorial inflation of the magnetosphere and consequently the magnetopause. Empirical studies using Voyager and Pioneer data concluded that the kronian magnetopause was Earth-like in terms of its dynamics (Slavin et al., 1985) as revealed by how the position of the magnetopause varies with dynamic pressure. In this paper we present a new pressure-dependent model of Saturn's magnetopause, using the functional form proposed by Shue et al. (1997). To establish the pressure-dependence, we also use a new technique for fitting a pressure-dependent model in the absence of simultaneous upstream pressure measurements. Using a Newtonian form of the pressure balance across the magnetopause boundary and using model rather than minimum variance normals, we estimate the solar wind dynamic pressure at each crossing. By iteratively fitting our model to magnetopause crossings observed by the Cassini and Voyager spacecraft, in parallel with the pressure balance, we obtain a model which is self-consistent with the dynamic pressure estimates obtained. We find a model whose size varies as ~Dp-1/4.3 and whose flaring decreases with increasing dynamic pressure. This is interpreted in terms of a different distribution of fields and particles stresses which has more in common with the jovian magnetosphere compared with the terrestrial situation. We compare our model with the existing models of the magnetopause and highlight the very different geometries. We find our results are consistent with recent MHD modeling of Saturn's magnetosphere (Hansen et al., 2005).