An effective alternative to mechanical processing in the manufacture of metal parts with complex geometry is arc surfacing with layer-by-layer cladding by a 3D printer or robotic system. During arc cladding of thin-walled metal parts with complex geometries, there is a necessity to program the welding mode due to the heating of the workpiece during multilayer cladding, as well as high sensitivity to parameter deviations. The objectives of programming and tolerance estimation should be achieved on the basis of physical and mathematical modeling of the surfacing pool. The complexity of such modeling is caused by the intense curving of the pool surface during additive cladding. It is offered to use a special cylindrical coordinate system to describe the pool surface under cladding. Computer simulation of multilayer thin wall surfacing showed satisfactory compliance of the simulated form with the real life surface of the weld bead.