Abstract: By spherical function expansion of the scattered sound field in conjunction with rigid boundary conditions, formulas for reconstructing the shapes of rigid scattering objects are derived. These formulas are then used to reconstuct the shapes of spheres and ellipsoids of different eccentricities. The calculated results agree well with spheres and ellipsoids of small eccentricities. Deviations become evident for ellipsoids of larger eccentricities. The cause of the deviations are analysed.