Bulk, high temperature superconductors have significant potential for use as powerful permanent magnets in a variety of practical applications due to their ability to trap record magnetic fields. In this paper, soft ferromagnetic sections are combined with a bulk, large grain Y-Ba-Cu-O (YBCO) high temperature superconductor to form superconductor/ferromagnet (SC/FM) hybrid structures. We study how the ferromagnetic sections influence the shape of the profile of the trapped magnetic induction at the surface of each structure and report the surface magnetic flux density measured by Hall probe mapping. These configurations have been modelled using a 2D axisymmetric finite element method based on the H-formulation and the results show excellent qualitative and quantitative agreement with the experimental measurements. The model has also been used to study the magnetic flux distribution and predict the behaviour for other constitutive laws and geometries. The results show that the ferromagnetic material acts as a magnetic shield, but the flux density and its gradient are enhanced on the face opposite to the ferromagnet. The thickness and saturation magnetization of the ferromagnetic material are important and a characteristic ferromagnet thickness d* is derived: below d*, saturation of the ferromagnet occurs, and above d*, a weak thickness-dependence is observed. The influence of the ferromagnet is observed even if its saturation magnetization is lower than the trapped flux density of the superconductor. Conversely, thin ferromagnetic discs can be driven to full saturation even though the outer magnetic field is much smaller than their saturation magnetization.