In the present study, the flow–structure interaction of a starting jet through a flexible nozzle is experimentally investigated, with a focus on the optimal flexibility for thrust generation. Water slug is impulsively accelerated through a cylindrical nozzle, fabricated with silicone rubber of varying flexibility. In general, the flexible nozzle modifies the vortical structure of the jet and augments the thrust of the starting jet. The measurement of nozzle surface deformation revealed that a back-and-forth wave propagation on the nozzle surface is responsible for the jet-vortex evolution augmenting the thrust generation. Combining the hydrodynamic conservation equations and the linearized shell theory, we also formulated the governing equations, dominated by two relevant dimensionless parameters: the effective acceleration time of the jet ( $\varPi _0$ ) and the effective nozzle stiffness ( $\varPi _1$ ). Asymptotic analysis of the equation showed that the dimensionless wave speed ( $\hat {c}$ ) is expressed as $\hat {c}=(\varPi _{0}^{2}\varPi _{1}/2)^{0.5}$ , and the jet momentum is maximized at $\hat {c}=\hat {c}_{crit}$ ( $\simeq 3.0$ ), the condition at which the release of elastic energy stored during nozzle contraction to the jet is synchronized with the instant of termination of jet acceleration. While $\hat {c}=\hat {c}_{crit}$ , the achievable maximum jet velocity decreases with the effective acceleration time of the jet ( $\varPi _0$ ), which is attributed to the reduced speed of the surface wave by the flow inside the nozzle.