This paper presents an analytical model for the aeroelastic instability of an infinitely long cylindrical shell in cross flow. The mean flow field is represented by a free-streamline model, and the perturbation flow field by a velocity potential associated with deformation of the shell cross-section; motions of the shell are described by Flügge's two-dimensional equations. It is shown that certain types of shell motions induce a negative aerodynamic damping, which increases with flow velocity; for sufficiently high flow, it overcomes the positive dissipative damping of the system, precipitating flutter, sequentially in the second, third and higher circumferential modes of the shell – each with specific orientation of the nodal pattern with respect to the free-stream vector. These analytical predictions are in agreement with observations in wind-tunnel experiments; quantitatively, predicted and measured flow-velocity instability thresholds are of the same order of magnitude.