The paper studies an integrated starter-generator based on a synchronous machine with PM excitation (ISG), used to start an internal combustion engine (ICE) of an autonomous energy facility or vehicle and supply electric energy to its consumers. The purpose of the work is to obtain a mathematical model of the starting mode in the form of a system of differential equations, its virtualization by means of the Matlab Simulink package and a diesel engine starting simulation using ISG with the study of the starting process dynamic characteristics. It is also required to carry out experimental verification of theoretical results through field tests of a prototype starter-generator to confirm the mathematical model adequacy. Difficulties in the analysis and synthesis of ISG are due to the complexity of electromechanical energy conversion processes in it and the trapezoidal nature of the magnetic field spatial distribution in the gap, which was established when solving the magnetostatic problem by the finite element method. These features make it difficult to use traditional research methods. The mathematical model of the operation starting mode, obtained under a number of assumptions that do not affect the nature of electromechanical processes, makes it possible to investigate the ICG static and dynamic characteristics during the electric start of the internal combustion engine. The ISG start-up process simulation was carried out on the basis of equations describing the starter operation using control systems both without starting current limitation and with limitation and providing a sufficient starting torque. Modeling made it possible to determine the start duration and the change of the electromagnetic torque, inverter and winding currents. A prototype ISG was designed and manufactured. Full-scale tests of the diesel engine electric start system were carried out. The results obtained confirmed the adequacy of the developed mathematical model and the possibility of its use in the study of the ISG other specific operating modes.