Numerical modelling of non-steady state laser-ablated flows is presented. Two simulation methods, the Monte Carlo technique and the large-particle (LP) method are used to investigate pulsed laser evaporation for different laser fluences under vacuum. Time-evolutions of the flow parameters are related to the evaporated material properties and laser pulse parameters. Non-Maxwellian time-of-flight (TOF) distributions are attributed to both non-stationary surface evaporation and inter-particle interactions in the laser plume. A radial surface temperature distribution was found to influence the plume shape. The influences of the experimental parameters on the TOF signal and on the plume shape are analyzed based on the Knudsen layer -unsteady adiabatic expansion model. The role of the evaporation yield, laser beam radius, initial plume length, and evaporation barrier in the formation of the angular distribution of the ablated material are discussed. The study concentrates on a better understanding of pulsed laser deposition (PLD).