Cell biophysical properties are a new class of biomarkers that can characterize cells into subgroups that indicate differences in phenotypes that may correlate with disease and cell state. Microfluidic biophysical cell sorters are platforms that utilize these newly developed biomarkers to expand biomedical capabilities for improvements in cell state detection and characterization. Cell biophysical properties are important indicators for cell state and function because they point to differences in cell structures, such as cytoskeletal arrangement and nuclear content. In particular, some diseases, such as cancer and malaria, can cause significant changes in cell biophysical properties. Therefore, cell biophysical properties have the potential to be used for disease diagnostics. Microfluidic systems which can interrogate these biophysical properties and exploit changes in biophysical properties to separate cells into subpopulations will provide important biomedical capabilities. In this combined theoretical and experimental investigation, we explore a new type of cell sorter which utilizes differences in biophysical properties of cells. These biophysical properties that can be utilized to sort cells include size, elasticity and viscosity. We invented a microfluidic system for continuous, label-free cell separation that utilizes variations in cell biophysical properties. A microfluidic channel is decorated by periodic diagonal ridges that are designed to compress flowing cells in rapid succession. The physical compression, in combination with hydrodynamic secondary flows induced by the ridged microfluidic channel, translates each cell perpendicular to the channel axis in proportion to its biophysical properties. Through careful experimental and computational studies, we found that the cell trajectories in the microfluidic cell sorter correlated to these biophysical properties. Furthermore, we examine the effect of channel design parameters under various experimental conditions to derive cell separation models that can be used to qualitatively predict cell sorting outcome. A variety of biophysical measurement tools, including atomic force microscopy and high-speed optical microscopy are used to directly characterize the heterogeneous population of cells before and after separation. Taken together, we describe the physical principles that our microfluidic approach can be effectively used to separate a variety of cell types. The major contribution is the creation and characterization of a novel microfluidic cell- sorting platform that utilizes cell biophysical properties to enrich cells into phenotypic subtypes. This innovative approach opens new ways for conducting rapid and low-cost cell analysis and disease diagnostics through biophysical markers.