The sound radiation of a loudspeaker on a sound bar with a slender shape is analyzed. Measurements and boundary element method (BEM) simulations of a rectangular rigid enclosure with a flat piston turn out to be in close agreement up to the frequency limit imposed by the discretization chosen for the BEM. Looking up for a shorter computation time, we consider an analytic model based on a geometrical approximation of the sound bar by a prolate spheroid. The corresponding spheroidal coordinate system allows for an analytical solution of the sound-radiation problem. The following parameters are adjusted: geometry of the ellipse-based spheroid, size and location of the circular piston, minimum order of the spheroidal wave functions that ensures convergence. In the light of the BEM results, we also predict the frequency validity of the analytic model. In order to improve the control of the acoustical field radiated by a sound bar, we discuss the influence of the enclosure edges on the regularity of the sound field pattern. [Work supported by the ANR-13-CORD-0008 EDISON 3D grant from the French National Agency of Research.]