A robust numerical method based on smoothed particle hydrodynamics (SPH) is developed for simulations of laser melting of metals and melt pool dynamics. The method accounts for all major interfacial effects, including surface tension, Marangoni stress, recoil force due to vapor pressure, as well as mass removal and cooling due to evaporation. The developed SPH method is combined with a classical ray tracing method for prediction of propagation and absorption of laser radiation. The optimum values of artificial viscosity coefficient and number of SPH particles for developed method are found in preliminary simulations of the keyhole drilling by a continuous wave laser. The method is then used to study melt expulsion from a keyhole during laser drilling in two-dimensional simulations. It is also shown that the method can be used to predict the keyhole formation and material binding in selective laser melting of metal powders.