Uranium-based intermetallic compounds often display very strong magnetic anisotropies, the energy of which is usually not directly accessible by common experimental methods. Here, we report on static- and pulsed-field studies of U3Cu4Ge4. This material orders ferromagnetically at TC=73K with the easy magnetization direction along the a axis and a strong bc-plane anisotropy. The magnetization measured for fields along the hard b direction displays a first-order magnetization process that can be described well by use of a phenomenological theory yielding anisotropy constants up to the sixth order. This phenomenological description, working excellently for U3Cu4Ge4, may also be applied for other uranium-based compounds.