Physical processes occurring in the keyhole during the deep-penetration laser welding of aluminium, where evaporation, ionization and formation of near-surface low-temperature plasma can take place, are studied theoretically. Equations of radiation gas dynamics including the equilibrium model of plasma, description of laser radiation transport and absorption are solved. Numerical calculations of plasma cloud propagation processes in aluminium vapour are performed in a one-dimensional approach. The minimum radiation power necessary to maintain this cloud is found. The effect of radiation trapping by plasma due to self-absorption in the optically thick plasma layer is revealed. The simulation results are of interest for a qualitative understanding of the processes in the keyhole plasma.