jats:pWe demonstrate, at room temperature, the strong coupling of the fundamental and non-uniform magnetostatic modes of an yttrium iron garnet ferrimagnetic sphere to the electromagnetic modes of a co-axial cavity. The well-defined field profile within the cavity yields a specific coupling strength for each magnetostatic mode. We experimentally measure the coupling strength for the different magnetostatic modes and, by calculating the expected coupling strengths, we are able to identify the modes themselves.</jats:p>