The problem of separation of uranium isotopes in a concurrent gas centrifuge is solved analytically. Separative power of the optimized concurrent gas centrifuges equals to $δU=12.7(V/700~{\rm m/s})^2 (300 ~{\rm K}/T)L, ~{\rm kg ~SWU/yr}$, where $L$ and $V$ are the length and linear velocity of the rotor of the gas centrifuge, $T$ is the temperature. This formula well agrees with an empirical separative power of counter current gas centrifuges. The optimal value of the separative power is not unique on the plane $(p_w,v_z)$, where $p_w$ is pressure at the wall of the rotor and $v_z$ is axial velocity of the gas. This value is constant on a line defined by the equation $p_wv_z=constant$. Equations defining the mass flux and the electric power necessary to support the rotation of the gas centrifuge are obtained.

18 pages, 2 figures