<p>Collective cell and tissue migration is crucial for various biological processes, including morphogenesis, wound healing, and cancer metastasis. Migrating cell monolayers often exhibit complex viscoelastic responses and coexistence of solid and liquid-like behaviors that are not well understood in the framework of existing theories. Here, we introduce a partial fluidization approach for collective cell migration. We treat the cell monolayer as a single albeit spatially and temporally non-uniform phase bridging two distinct states: a viscous liquid and a soft solid with an elastic response to shear. The continuous transition between these states is controlled by the fluidization order parameter that, in turn, depends on the normalized shear stress. The model successfully captures key experimental observations: solid-like plug flow of cells in a microfluidic channel, spatial coexistence of moving and immobile domains in cell monolayers, and solid body-like rotational flow of cells in a circular chamber. The approach provides insights into the physical mechanisms of cell migration. It can be extended to more realistic situations, such as confluent monolayers on curved, compliant, or degradable surfaces as well as three-dimensional proliferating tissues and chemical signaling.</p>