Analysis is given for nonstationary propagation of rotating ion beam which has a finite length on the basis of Vlasov–Maxwell equations. The beam velocity distribution function is assumed to have a form of product of a modification function g which depends on time and axial coordinate multiplied by a steady solution f_b0 which is a known function of particle velocity and radial coordinate. Unknown function g is solved as the solution of Vlasov equation through electromagnetic fields induced by leading and trailing edges. These electromagnetic fields can be solved from the Maxwell equations by using beam distribution function and motion of electrons in background plasma.