Cytoskeletal mechanics regulates cell morphodynamics and many physiological processes. While contractility is known to be largely RhoA-dependent, the process by which localized biochemical signals are translated into cell-level responses is poorly understood. Here we combine optogenetic control of RhoA, live-cell imaging and traction force microscopy to investigate the dynamics of actomyosin-based force generation. Local activation of RhoA not only stimulates local recruitment of actin and myosin but also increased traction forces that rapidly propagate across the cell via stress fibres and drive increased actin flow. Surprisingly, this flow reverses direction when local RhoA activation stops. We identify zyxin as a regulator of stress fibre mechanics, as stress fibres are fluid-like without flow reversal in its absence. Using a physical model, we demonstrate that stress fibres behave elastic-like, even at timescales exceeding turnover of constituent proteins. Such molecular control of actin mechanics likely plays critical roles in regulating morphodynamic events.