The dynamic behaviour of composites containing long soft fibers of elliptic cross section is studied in the frequency range where the material behaves as a meta-material. The results of homogenization theory for composites containing soft inclusions are recalled, showing the conditions that lead to a frequency dependent dynamic density coming from the inner resonance of soft inclusions. The dynamic density is expressed from the resonance frequencies and participation factors of the inner inclusions obtained by solving a localization problem. The solution to this problem is obtained for a composite containing long fibers of elliptic cross section by using an expansion into Mathieu functions. The set of resonance frequencies and participation factors can be split into different subsets corresponding to the different symmetries of localization problems related to different directions of the macroscopic acceleration. All results are found to be consistent with the extreme cases of aspect ratios corresponding to stratified media (plane inclusions) and circular fibers.