The process of fission of charged liquid droplets is an important stage of multiply charged ion formation in the electrospray ionization (ESI) process. ESI is currently the most powerful ionization method in the mass spectrometry of large molecules such as biopolymers. Fission plays a crucial role in the ion formation essentially in the range of nanosized droplets, since it determines the charge states of product ions. Usually the Rayleigh equation is used to determine critical conditions, at which the fission process takes place. This equation gives the value of the critical radius of the charged droplet as a function of its charge and specific surface energy. The Rayleigh equation does not give us the opportunity to determine charges and sizes of the fission fragments. In the present work we propose a mathematical model that describes the fission process of the charged liquid droplet in an external electrostatic field. The model is based on the quasi-equilibrium assumption that the most probable shape of the droplet corresponds to the minimum of the free energy of the system. The change in the internal kinetic energy and dissipative losses for the viscous liquid are also taken into account in the model.