Very little attention has been given, so far, to the problem of the propagation of axisymmetric second‐sound shock waves, although they may occur in practical applications. In this paper, research on the propagation of moderate cylindrical heat pulses in superfluid helium is reported. A theoretical model is built based on the experimental observation of the evolution of the structure of rectangular heat pulses. The agreement between the experimental measurements and the theoretical calculations of the evolution of the main parameters is very satisfactory.