A review study of the developments in the field of pulsed laser-solid interaction simulation methods, for moderate laser energies, is presented. The paper is focused on the methods that numerically simulate the interactions of pulsed ns-laser with solid metal targets. Three main regimes for pulsed laser excitation, are well established, namely, the thermoelastic, melting and plasma regimes. The modelling and simulation techniques that may numerically describe these three regimes and the occurring dynamic matter responses are reviewed. Modelling efforts concerning various fields of applications of lasers are briefly discussed.