DNA elongation induced by fluidic stress was investigated on a microfluidic chip composed of a large inlet pool and a narrow channel. Through single-DNA observation with fluorescence microscopy, the manner of stretching of individual T4 DNA molecules (166 kbp) was monitored near the area of accelerating flow with narrowing streamlines. The results showed that the DNA long-axis length increased in a sigmoidal manner depending on the magnitude of flow acceleration, or shear, along the DNA chain. To elucidate the physical mechanism of DNA elongation, we performed a theoretical study by adopting a model of a coarse-grained nonlinear elastic polymer chain elongated by shear stress due to acceleration flow along the chain direction.