The authors present the design and optimization of an optofluidic monolithic chip, able to provide optical trapping and controlled stretching of single cells. The chip is fabricated in a fused silica glass substrate by femtosecond laser micromachining which can produce both optical waveguides and microfluidic channels with great accuracy. A new fabrication procedure adopted in this work allows the demonstration of microchannels with a square cross-section, thus guaranteeing an improved quality of the trapped cell images. Femtosecond laser micromachining emerges as a promising technique for the development of multifunctional integrated biophotonic devices that can be easily coupled to a microscope platform, thus enabling a complete characterization of the cells under test.