The effect of a non-zero shear modulus on two-dimensional acoustic cloaking based on the transformation technique is investigated. Using the method of multiple scales, approximate solutions are found to the elastic equations with anisotropic density when the ratio of the shear modulus to the bulk modulus is small. These solutions indicate that a non-zero shear modulus causes the cloaking effect to become limited to a band of frequency, which becomes wider as the shear modulus is reduced. Resonances associated with shear waves are seen in the tangential component of displacement but do not affect the scattering to first order in the asymptotic expansions. No finite solutions exist for the case when the transformation shrinks the cloaked object to zero size (perfect cloaking).