We present an efficient method for measuring cell stretching based on three-dimensional viscoelastic particle focusing. We suspended cells in a biocompatible viscoelastic medium [poly(vinylpyrrolidone) solution in phosphate-buffered saline]. The medium viscoelasticity significantly homogenized the trajectories of cells along the centerline of a simple straight channel, which could not be achieved in conventional Newtonian media. More than 95% of red blood cells (RBCs) were successfully delivered to the stagnation point of a cross-slot microchannel and stretched by extensional flow. By computational simulations, we proved that this method prevents inaccuracies due to random lateral distributions of cells and, further, guarantees rotational-free cell stretching along the shear-free channel centerline. As a demonstration, we characterized the differences in RBC deformabilities among various heat treatments. Furthermore, we monitored the decrease of deformability due to nutrient starvation in human mesenchymal stem cells. We envisage that our novel method can be extended to versatile applications such as the detection of pathophysiological evolution in impaired RBCs due to malaria or diabetes and the monitoring of cell quality in stem cell therapeutics.