Adherent cells perceive mechanical feedback from the underlying matrix and convert it into biochemical signals through a process known as mechanotransduction. The response to changes in the microenvironment relies on the cell’s mechanical properties, including elasticity, which was recently identified as a biomarker for various diseases. Here, we propose the design, development, and characterization of a new system for the measurement of adherent cells’ strain drop, a parameter correlated with cells’ elasticity. To consider the interplay between adherent cells and the host extracellular matrix, cell stretching was combined with adhesion on substrates with different stiffnesses. The technique is based on the linear stretching of silicone chambers, high-speed image acquisition, and feedback for image centering. The system was characterized in terms of the strain homogeneity, impact of collagen coating, centering capability, and sensitivity. Subsequently, it was employed to measure the strain drop of two osteosarcoma cell lines, low-aggressive osteoblast-like SaOS-2 and high-aggressive 143B, cultured on two different substrates to recall the stiffness of the bone and lung extracellular matrices. Results demonstrated good substrate homogeneity, a negligible effect of the collagen coating, and an accurate image centering. Finally, the experimental results showed an average strain drop that was lower in the 143B cells in comparison with the SaOS-2 cells in all the tested conditions.