A computational study of rigidity for dense fluids of monodisperse and bidisperse hard-disks near a phase and a glass transition respectively is presented. To achieve this goal, the transversal part of the dynamical structure factor is calculated. In both cases, a viscoelastic behavior is obtained, with a dynamical gap determined by a critical wavevector k c. Transversal waves exist for k > k c while the maximal correlations happens at frequency ω = 0 for k < k c. In both cases k c goes to zero as the freezing point is approached. Both systems are able to fulfill a scaled dynamical law as a power law is found for the critical k c as a function of the packing. The obtained results indicate that this method gives an alternative to study rigidity and constraint theory in dense fluids, since it is possible to assign a number of floppy modes or broken constraints in the liquid by computing the number of modes below k c , as well as an effective average coordination number. Also, this suggests that the critical wavevector k c can serve as a suitable order parameter.