The asymptotic self‐similar form of cylindrically or spherically imploding shock waves is extracted by numerically solving non‐self‐similar problems. The shock wave is generated by a contracting piston with finite initial velocity. For the initial shock motion, a perturbation method is used to determine the starting condition for the numerical calculation. Propagation of the shock wave and flow field properties are obtained and the transition of the non‐self‐similar motion of the shock wave into the self‐similar one is presented. Good agreement between self‐similar exponents determined from the variation of the shock strength and those calculated by Guderley is obtained.