Extending the propagation formula of the attenuated laser-induced plasma shock wave front with spherical symmestry in the air to the non-absolute centric symmetry is described in this paper. According to the analysis of the measured data for the laser-induced plasma shock wave front by using photo shadowgraph, a propagation formula of a rotational ellipsoid shock wave for a point source in the laser-induced plasma in a liquid is presented in this paper.The shock wave attenuation in pure water and ethanol has been investigated by means of the acoustic method. The experimental data are in agreement with the calculated results.