The hydrodynamic start-up problem is one of the most crucial issues in laser-driven symmetrical implosion. The target-surface roughness and initial imprint by nonuniform laser irradiation result in Rayleigh–Taylor instability in the acceleration and deceleration phase. To estimate the tolerance of the target-surface roughness, the temporal behaviour of corrugated ablation surface and rippled shock-wave propagation are investigated using a perturbation analysis of the fluid equation, which is solved under the boundary model of a fire-polished ablation surface. The results show good agreement with two- dimensional hydrodynamic simulation and experimental results [T. Endo et al., Phys. Rev. Lett. 74, 3608 (1995)].