In this paper an analytical solution as a separable function of azimuth angle and axial dimension is presented in order to calculate the acoustic radiation patterns from a finite source of uniform amplitude, vibrating sinusoidally, on a rigid elliptic cylinder of infinite length. The approximate solution at far field is obtained by the saddle-point method. It is shown that the pattern in a plane orthogonal to the axis of the elliptic cylinder is independent of the axial distribution of the source, and is identical to the pattern for a source of infinite axial extent. Acoustic radiation patterns in the planes, orthogonal to and containing the axis of the elliptic cylinder, and acoustic radiation impedance are computed numerically for the particular cases in which a finite source located on the major and/or minor axis of the ellipse. Acoustic radiation characteristics of azimuth and axial extent of the source is discussed in comparison with point source approximation.