Point absorbers are one of the most common wave energy converters, which are typically designed to extract power primarily from heave motion. Pure heave motion of an axisymmetric wave energy converter results in a relative capture width limited to a third of the maximum possible. Over the past few decades, an increasing amount of attention has been given to the design of point absorbing wave energy converters operating in multiple oscillation modes, in an attempt to more efficiently extract power from waves. However, it is not a trivial task as wave energy converters operating in multiple modes demonstrate complex coupled vibrational characteristics across several degrees of freedom. This paper addresses this challenge using modal analysis, a modern approach developed for determining, improving and optimising dynamic characteristics of complex engineering systems. Case studies are conducted on three multi-mode submerged point absorber designs, each with distinct modal behaviour to show the generality and efficacy of the approach. Results show that in combination with knowledge of wave power absorption in the frequency-domain, modal analysis can be used as an effective analytical tool to evaluate the vibrational characteristics and the power absorption potential of the multi-mode system, as well as to explore the corresponding working principles and the physical limits of the design.