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 vapor. 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 vapor, however, is solved analytically 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 effects of the laser intensity, back temperature and back pressure are analyzed. The temperature, pressure, density and velocity of the laser induced vapor are calculated and the results are discussed.