Although collective cell migration (CCM) is a highly coordinated and ordered migratory mode, perturbations in the form of mechanical waves appear even in 2D. These perturbations caused by the viscoelastic nature of cell rearrangement are involved in various biological processes, such as embryogenesis, wound healing and cancer invasion. The mechanical waves, as a product of the active turbulence occurred at low Reynolds number, represent an oscillatory change in cell velocity and the relevant rheological parameters. The velocity oscillations, in the form of forward and backward flows, are driven by: viscoelastic force, surface tension force, and traction force. The viscoelastic force represents a consequence of inhomogeneous distribution of cell residual stress accumulated during CCM. This cause-consequence relation is considered on a model system such as the cell monolayer free expansion. The collision of forward and backward flows causes an increase in cell packing density which has a feedback impact on the tissue viscoelasticity and on that base influences the tissue stiffness. The evidence of how the tissue stiffness is changed near the cell jamming is conflicting. To fill this gap, we discussed the density driven change in the tissue viscoelasticity by accounting for the cell pseudo-phase transition from active (contractile) to passive (non-contractile) state appeared near cell jamming in the rheological modeling consideration.