The purpose of the article is to analyze perturbations of the acoustic cloaking shell parameters described recently by Cummer et al. It is shown that infiniteness of density and stiffness is not required for zero acoustic scattering. The problem of 3D acoustic cloaking shell is found to be robust. Based on the general approach (metric transformations) proposed in 1961 by the Russian scientist Lev Dolin we present an alternative realization of the acoustic cloaking shell with higher flexibility of the cloaking shell parameters.