The starburst galaxy M82 shows a system of Hα-emitting filaments that extend to each side of the galactic disk. We model these filaments as the result of the interaction between the winds from a distribution of super stellar clusters (SSCs). We first derive the condition necessary for producing a radiative interaction between the cluster winds (a condition that is met by the SSC distribution of M82). We then compute three-dimensional (3D) simulations for SSC wind distributions that satisfy the condition for a radiative interaction, as well as for distributions that do not satisfy this condition. We find that the highly radiative models, which result from the interaction of high-metallicity cluster winds, produce a structure of Hα-emitting filaments that qualitatively agrees with the observations of M82, while the nonradiative SSC wind interaction models do not produce filamentary structures. Therefore, our criterion for radiative interactions (which depends on the mass-loss rate, the terminal velocity of the SSC winds, and the mean separation between the SSCs) can be used to predict whether or not an observed galaxy should have associated Hα-emitting filaments.