This work examines the characteristic differences in acoustic scattering between air-filled double-layered encapsulating (DLE) shells and air-filled single-layered encapsulating (SLE) shells. The analysis shows that the presence of an outer layer softer than the inner layer results in a shift of the first monopole of the reflectivity-frequency response to a higher frequency and a reduction in the monopole peak; and it leads to a frequency-separation of the two dipoles that trace the monopole. The frequency shift and the peak reduction of the monopole and the frequency separation of the two dipoles all increase with the increasing thickness of the softer outer layer. The numerical results reveal that variations in the Lame constant of the model material for the protein albumin have little effect on the low-frequency scattering characteristics, while they affect the high-frequency scattering characteristics significantly. The authors have shown that this phenomenon is due to the fact that the model material for the protein albumin has a Lame constant substantially larger than its shear modulus. Their further numerical studies conclude that, for each DLE shell, one can construct an equivalent SLE shell, using a simple scheme originated from the mechanics of composite materials in the sense that the so-constructed SLE shell has essentially the same acoustic scattering characteristics as the DLE shell within a low frequency range.