Multiple analytical models of the laser metal deposition process have been presented, but most rely on sequential solution of the energy and mass balance equations presented. Discretization of the problem domain using finite element or similar code is typically used where a fully coupled mass-energy balance solution is required, but the multiphase nature of the process means it is difficult to establish an easily applied model of track geometry via this method. In this work a coupled analytical solution is presented. Sub-models of the powder stream, quasi-stationary conduction in the substrate, and powder assimilation into the area of the substrate above the liquidus temperature, allowing for surface geometry factors, are combined. An iterative feedback loop is used to ensure mass and energy balances are maintained at the melt pool. The model predictions show good agreement with experimental melt pool temperatures and Ti-6Al-4V deposited single tracks, produced with a coaxial nozzle and a Laserline 1.5 kW diode laser. The model is a useful industrial aid and alternative to finite element methods for selecting the parameters to use for laser direct metal deposition.