Controlling the interaction of particulate drug delivery systems with biological cells and tissues is critical for the success of therapies. Specifically in cancer, due to the high density of tumor tissues, drug penetration is critical and may be challenging. New methodology for nanoparticle drug carrier microfabrication using microfluidics allowing the tight control over particle properties. We show that tuning the mechanical properties of nanoparticles can affect their interaction and selectivity with single tumor cells and with 3D tumor aggregates. Using polymer micelles we provide a proof of concept that stiffer particles has an enhanced permeability cellular potential than flexible one. Detailed characterization of the nanoparticles, including examinations of particle size, stability, drug release kinetics and cell transcytosis, was performed in cancer cell lines and patient derived cells. A simple physical model is presented that well agrees with the experiments and provides insight about the role of particle rigidity in the engulfment mechanism. We conclude that particle rigidity enhances cellular uptake and tissue penetration and that polymer micelles have promising potential as an effective and highly permeable drug delivery system. Our results lay the ground for developing a scheme for a rational drug delivery based on the specific cues of the tumor tissue.