The dynamics of the radiative plasma expansion into an ambient gas is considered. The model describes the evolution of the plasma emission spectrum and the dynamics of the resulting shock wave. The time frame for the applicability of the model is in the tens of nanoseconds after the laser pulse is terminated, until a few microseconds later when the plasma ceases to emit. It is assumed that local thermodynamic equilibrium is established and that the plume expands with spherical symmetry. The model outputs are spatial and temporal distributions of atoms, ions, and electron number densities, evolution of atom and ion line profiles, and the shock wave. The model should be applicable to spectroscopic analysis of the initial plasma state and plasma dynamics.