Laser ablation consists of three coupled processes: (i) heat conduction within the solid, (ii) flow through a discontinuity layer (evaporation wave) attached to the solid surface, and (iii) shock wave expansion of the laser induced plume. In this paper, a one-dimensional solution for all three coupled processes is presented. The heat conduction and the evaporation wave are solved numerically. The shock wave expansion of the laser induced plume, however, is solved analytically, to our knowledge, for the first time; analytical solutions for the classic Riemann problem have been employed to solve the transient propagation of the strong shock wave. This model provides a sound theoretical basis for the analysis of the laser ablation process. The temperature, pressure, density, and velocity of the laser induced plume at different laser intensities, back temperatures, back pressures, and ambient gas species are calculated. The effects of the laser intensity, back temperature, back pressure, and ambient gas species are analyzed. The theoretical results provide insight into experimental results available in the literature.