A study of the possible axisymmetric modes that propagate at low frequencies in buried, water-filled iron pipes is presented. It is well known that for a vacuum-pipe-vacuum system the sole non-torsional axisymmetric mode that exists at low frequencies is the fundamental L(0,1) mode. When a pipe is filled with water and still surrounded by a vacuum it is also known that another mode then appears which at low frequencies is characterized by predominantly axial water-borne displacements. In addition to these modes, this paper explores two other, less well known axisymmetric modes whose existence depends on the acoustic properties of the outer medium that surrounds a pipe. In this paper the predicted characteristics of these modes are presented.