The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. It is shown that to second order in k 0 a (k 0 the wavenumber in the host medium, a the radius of the cylinder), only the first three terms (i.e., of orders 0, -1 and +1) in the partial wave representation of the scattered field are non-vanishing, and the material parameters enter into these terms in explicit manner. Moreover, the zerothorder term contains only two of the unknown material constants (i.e., the real and imaginary parts of complex compressibility of the cylinder κ 1 ) whereas the ±1 order terms contain the other material constant (i.e., the density of the cylinder ρ 1 ). A method, relying on the knowledge of the totality of the far-zone scattered field and resulting in explicit expressions for ρ 1 and κ 1 , is devised and shown to give highly-accurate estimates of these quantities even for frequencies such that k 0 a is as large as 0.1.