An analytical heat transfer model has been development and applied for calculating the shape of the solid thickness profile for continuous casting of thin metal rods. The stationary solidification front relative to the crystallizer was received from superposition of the motions of the liquid metal flow in the axial direction and the solidifying metal in the radial direction. The shape of the solidified crust depends on several parameters. The influence of the contact layer between the frozen crust and the internal surface of a crystallizer on the solidification process is also studied. The results are presented as an analytical model and are graphically shown for different selected parameters.