With the fast development of acoustic systems in clinical and therapeutic applications, acoustically driven microbubbles have gained a prominent role as powerful tools to carry, transfer, direct, and target drug molecules in cells, tissues, and tumors in the expanding fields of targeted drug delivery and gene therapy. The aim of the present study is to establish a biocompatible acoustic microfluidic system and to demonstrate the generation of an acoustic field and its effects on microbubbles and biological cells in the microfluidic system. The acoustic field creates non-linear oscillations of the microbubble-clusters, which results in generation of shear stress on cells in such microsystems. This effectively helps in delivering extracellular probes in living cells by sonoporation. The sonoporation is investigated under the combined effects of acoustic stress and hydrodynamic stress during targeted drug and gene delivery.