The goal of the current work is to perform numerical modeling and identify important phenomena associated with vapor plume and jet flows induced by irradiation of metal targets with short pulse or continuous wave (CW) lasers, discover and explain the mechanisms responsible for vaporized material motion in applications of lasers for material processing and analysis such as deep laser drilling, laser-induced breakdown spectroscopy (LIBS), and selective laser melting (SLM) of metallic powders. The simulations of laser-induced vapor expansion into a background gas are performed with a combined computational model, including the thermal model of irradiated targeted and a kinetic model of multi-component gas flows. The latter is implemented for simulations in the form of the Direct Simulation Monte Carlo method. Based on this model, two major problems are considered. In the first problem, vapor plume expansion under conditions of spatial confinement when the plume, which is induced by irradiation of a copper target by a short-pulse laser, propagates inside a cavity or trench, is considered. The simulations identify two major effects, the focusing effect, appearing due to transient motion of shock waves inside the cavity, and the confinement effect, induced due to overall deceleration of the plume with increasing background gas pressure, as two major mechanisms affecting removal of vaporized material out of the cavity and formation of high-density and high-temperature regions in the plume core. Due to the trade-off between these effects, an optimum background gas pressure exists, when the efficiency of the vapor removal from the cavity is maximized. At later stages of plume expansion, the simulations also reveal a suction effect, when the vapor flow at the cavity throat can be temporarily directed into the cavity, inducing a decrease of the overall efficiency of vapor removal. The balance between the focusing and confinement effects is studied in a range of the background gas pressure, for various background gas species, and various geometrical parameters of the cavity and laser beam. It is also shown that application of double laser pulses with short inter-pulse separation can be beneficial for both laser drilling and LIBS. In the second problem, a vapor jet induced by irradiation of a stainless steel target by a CW laser is simulated under conditions specific for SLM of metallic powders. The generated vapor jet is then used to predict motion of powder particles that can be efficiently entrapped into the ambient gas flow induced by the vapor jet. It is shown that powder particles in a broad range of their diameters can be efficiently entrained into the gas flow and, thus, removed from the irradiated surface. These results are in agreement with experimental observations of the surface denudation effect in SLM.