In this article, we describe the design of a shape memory alloy-based system to stretch cells cultured on top of a flexible membrane in multi-directions (longitudinal and transverse). Mechanical cues (such as strain and force) can affect the state and behavior of cells, such as, morphology, the differentiation process, and apoptosis. Therefore, a thorough understanding of the effects of mechanical perturbations on cells/tissues will have a deep impact in the biological sciences. The proposed design allows application of anisotropic (multi-axial) strain with high-precision. Certain cells, for example endothelial cells that line the inside of blood vessels, experience multi-axial (circumferential and longitudinal) stresses and strains. A cell stretching device that enables controlled application of biaxial strain will allow for systematic and accurate studies of the effects of externally applied mechanical perturbation throughout the cell, tissue, or organ. A preliminary design is proposed that exploits the strain recovery property of the shape memory alloy (SMA) actuators. We describe the design of the mechanical system and show experimental results to demonstrate stretching of a thin PDMS membrane in the longitudinal and transverse directions. To account for the inherent nonlinearity of the SMA, a feedback controller is implemented to achieve high-precision control of the stretching process. Additionally, the design can be integrated with an atomic force microscope (AFM) for high spatial and temporal resolution studies.