The acoustic radiation from an elastic cylindrical shell defined by nonconcentric cylindrical surfaces and submerged in an acoustic fluid is studied. The driving mechanism is a time‐harmonic internal pressure. In particular, the influence of the nonconcentricity parameter δ on the resulting radiation field is examined. The solution is obtained by means of an expansion in powers of this parameter about the concentric solution, δ=0. Each order of solution is solved in closed form by means of boundary integral equation methods. Results are given for the zeroth and first‐order solutions and it is seen that ajth driving mode will introduce nearest neighbor (j−1 andj+1) modes in the first‐order solution.