A linear theory of electrostatic ion cyclotron normal modes with moderate wavenumber (k⊥ &rgr;i≲1) which can exist in a sheared magnetic field is given. Such modes have been seen in a scattering experiment on the TFR tokamak. A novel mode with fluid electron behavior is found, and the Drummond and Rosenbluth current‐driven mode with kinetic electron behavior is recovered. Toroidal effects are considered. The kinetic modes offer the most natural explanation for the experimental frequency spectrum. However, numerical solutions of the dispersion relations predict that current drifts three to ten times larger than those in TFR are needed for instability.