Analytical modelling of a quasi-stationary laser melt pool without mass addition can be achieved using relatively simple moving surface heat flux solutions. However, including mass addition from a coaxial powder stream alters the laser flux and energy and mass flow pathways and often leads to the problem being modelled using numerical methods. The model described in this paper combines an analytical beam attenuation model to account for beam powder interaction above the melt pool with series of standard solutions for a moving Gaussian heat source to calculate melt pool size and substrate isotherms. A negative enthalpy method is used to compensate for the mass addition to the melt pool. The model is verified using a variety of methods and can predict powder stream mass and temperature distribution at the substrate and final melt pool shape in three dimensions from the major laser direct metal deposition process variables. The model highlights the role of beam-powder interaction in the process.