Application of a mathematical modelling of thermal plasma processes is effectively during development and optimization of electric power equipment as well as electro technological equipment. In the field of electric power industry such devices are: circuit breakers (simulation of arc extinction in the arc chamber); multi-chamber arresters for lightning protection of overhead power lines (simulation of arc discharge in a chamber of the arrester), and others. In the field of electro technological equipment such devices are: DC (and AC) arc plasma torches for air-plasma spraying of coating, metal welding and cutting; ICP (inductively coupled) plasma torches for nanomaterials production, fine powder treatment, plasma-chemical technologies and others. The article describes the main stages of the development of mathematical models: a study of the features of the physical process that allows us to formulate the basic assumptions of the model (stationary or non-stationary process, 2D or 3D geometry, laminar or turbulent flows and others); construction of the computational domain and of the mesh; setting the boundary conditions. Examples of results of calculations are shown. Recommendations on the use of specialized software are presented.