Shaping embryonic tissues requires spatiotemporal changes in genetic and signaling activity as well as in tissue mechanics. Studies linking specific molecular perturbations to changes in the tissue physical state remain sparse. Here we study how specific genetic perturbations affecting different posterior tissues during zebrafish body axis elongation change their physical state, the resulting large-scale tissue flows, and posterior elongation. Using a custom analysis software to reveal spatiotemporal variations in tissue fluidity, we show that dorsal tissues are most fluid at the posterior end, rigidify anterior of this region, and become more fluid again yet further anteriorly. In the absence of notochord (noto mutants) or when the presomitic mesoderm is substantially reduced (tbx16 mutants), dorsal tissues elongate normally. Perturbations of posterior-directed morphogenetic flows in dorsal tissues (vangl2 mutants) strongly affect the speed of elongation, highlighting the essential role of dorsal cell flows in delivering the necessary material to elongate the axis.