The complex ac susceptibility χ = χ′-j χ′′ of an infinitely long hard superconducting bar with an elliptical cross-section of semi-axes a and b is numerically calculated with a uniform ac field applied along the b axis, based on the critical-state model with a constant Jc. Normalized to the exact low-field limit of -χ′, χ0, -χ′ and χ′′ as functions of the field amplitude Hm normalized to the exact full penetration field Hp are given in tables and figures for 0.01≤b/a≤100. It is shown for any value of b/a that, with increasing Hm/Hp, χ′′ is proportional to and inversely proportional to Hm at and , respectively. Defining a characteristic point as where χ′′ takes its maximum χ′′m, it is shown that, with increasing b/a, χ′′m/χ0 increases from 0.188 to 0.229, whereas Hm(χ′′m)/Hp increases from 0.35 to 1.18 and -χ′(χ′′m)/ χ0 displays a minimum at b/a≈0.5. The results are used for comparing with some experimental data of a mono-filamentary Bi-2223/Ag tape. © 2005 IOP Publishing Ltd.