This paper presents an in-depth analysis of the scattering characteristics of the Cummer–Schurig acoustic cloaking design proposed by Cummer and Schurig (2007 New J. Phys. 9 45). The analysis uses an analytical solution for orthotropic media in conjunction with approximating the radially varying properties by multiple layers of uniform shells. The analysis shows that the cloaking is effective for both planar incident waves and line sources, but not perfect for the entire computed spatial frequency range up to ka=10, where k is the wavenumber in the host medium and a is the outer radius of the cloaking shell. Furthermore, the cloaking remains effective but less perfect when the cloaked region is not rigid. For a penetrable medium in the cloaked region, the cloaking is penetrated only at the resonant frequencies.