A possible plasma target for Magnetized Target Fusion (MTF) is a stable diffuse z-pinch in a toroidal cavity, like that in MAGO experiments. To examine key phenomena of such MTF systems, a magnetic flux compression experiment with this geometry is under design. The experiment is modeled with 3 codes: a slug model, the 1D Lagrangian RAVEN code, and the 1D or 2D Eulerian Magneto-Hydro-Radiative-Dynamics-Research (MHRDR) MHD simulation. Even without injection of plasma, high-Z wall plasma is generated by eddy-current Ohmic heating from MG fields. A significant fraction of the available liner kinetic energy goes into Ohmic heating and compression of liner and central-core material. Despite these losses, efficiency of liner compression, expressed as compressed magnetic energy relative to liner kinetic energy, can be close to 50%. With initial fluctuations (1%) imposed on the liner and central conductor density, 2D modeling manifests liner intrusions, caused by the m = 0 Rayleigh-Taylor instability during liner deceleration, and central conductor distortions, caused by the m = 0 curvature-driven MHD instability. At many locations, these modes reduce the gap between the liner and the central core by about a factor of two, to of order 1 mm, at the time of peak magnetic field.