Microfluidic devices for cell sorting or cell fractionation are disclosed. A microfluidic device can comprise one or more inlets, a first wall and a second wall, and two or more outlets. The first and second walls can be substantially planar to each other and the first wall having can have a plurality of ridges protruding from the first wall and defining a compression gap between the ridge and a surface of the second wall. The microfluidic device can also be a cell sorting device for sorting a plurality of cells based on one or more biophysical cellular properties including size, elasticity, viscosity, and/or viscoelasticity wherein the cells are subjected to one or more compressions due to the compression gap. Also disclosed are methods for cell sorting based on a variety of biophysical cellular properties.