The superradiant level shift of a system of N two-level molecules, interacting with the radiation field, is calculated for pencil-like geometry. Introducing the self-energy (N)(E) of the molecular systems due to its radiative interaction, we first discuss the trivial (N=1) and familiar (N=2) cases in more detail. The analytic properties of the self-energy (N)(E) are used to derive dispersion relations for its real and imaginary parts Δ(N)(E), Γ(N)(E). We then generalize to the case of N1, employing a self-consistency argument advanced by Arecchi and Courtens. The modified Dicke expression for the cooperative spontaneous decay rate is then used in the dispersion relation for the shift Δ(N) and a value of ∼6 MHz calculated corresponding to typical molecular-gas parameters. The physical measurability of the shift is discussed and a Brewer-Shoemaker experiment in a molecular gas is proposed for the observation of the shift. © 1973 The American Physical Society.