Electricity production is a major problem for deep space exploration. The possibility of using radioisotope elements with a very long life as an energy source was investigated in the framework of an EU project “SpaceTRIPS”. For this, a two-stage system was tested, the first in which thermal energy is converted into mechanical energy by means of a thermoacoustic process, and the second where mechanical energy is converted into electrical energy by means of a magnetohydrodynamic generator (MHD). The aim of the present study is to develop an analytical model of the MHD generator. A one-dimensional model is developed and presented that allows us to evaluate the behavior of the device as regards both electromagnetic and fluid-dynamic aspects, and consequently to determine the characteristic values of efficiency and power.