In a multi-wavelength study of thermal emission and scattered light images we analyse the dust properties and structure of the debris disc around the A1-type main sequence star 49~Cet. As a basis for this study, we present new scattered light images of the debris disc known to possess both a high amount of dust and gas. The outer region of the disc is revealed in former coronagraphic H-band and our new Y-band images from the Very Large Telescope SPHERE instrument. We use the knowledge of the disc's radial extent inferred from ALMA observations and the grain size distribution found by SED fitting to generate semi-dynamical dust models of the disc. We compare the models to scattered light and thermal emission data and find that a disc with a maximum of the surface density at 110~au and shallow edges can describe both thermal emission and scattered light observations. This suggests that grains close to the blow-out limit and large grains stem from the same planetesimal population and are mainly influenced by radiation pressure. The influence of inwards transport processes could not be analysed in this study.