In this work we study the localization of vibrational modes in heuristic models for disordered DNA-like molecules. Within such approach, atomic groups are replaced by renormalized sites connected by effective springs. The oscillation amplitudes at each site are considered and the localization degree of the normal modes is analyzed by means of the participation ratio, as well as the relative fluctuation of an ensemble of disorder realizations for normal modes in different frequency ranges. The present results suggest that the dynamical properties at low frequencies are completely different for double-strand structures compared to single-strand ones. Irrespective to disorder, double-strand molecules show normal modes with macroscopic localization lengths at low frequencies, for a wide range of spring constants considered in the literature, in contrast to the strong localization in single strands.