Gas turbine plants operated on a mixture of natural gas and air are widely used for self-contained power supply of buildings and structures both in urban conditions and in temporary settlements. When designing perspective gas turbine plants, we need to develop a non-toxic, environmentally friendly combustion chamber with the minimal emissions of harmful substances in a wide range of changes in operating parameters. It is a complicated engineering challenge to meet this condition: it is necessary to ensure geometrically accurate profiling of special holes in the cylindrical wall of the combustion chamber to insert fuel nozzles. As opposed to the known methods, the article proposes a profiling method, which combines the advantages of the known methods of descriptive geometry and precise methods of three-dimensional computer simulation. The real profile of a hole in the wall of the combustion chamber is a fourth-order spatial algebraic curve. The article proposes an algorithm for profile approximation using second-order curves by means of three-dimensional computer graphics, which allows us to streamline the preparation of a program for a water jet NC machine.