In this work multiple scattering by an array of perforated cylindrical shells with a porous core has been investigated. A semi-analytical model to predict scattering from such cylindrical units is presented in the context of the multiple scattering theory (MST), and validated against laboratory experiments. The suggested semi-analytical multiple scattering model uses an impedance expression to include the perforated shell in the scattering coefficients, which is a compact way to describe a composite scatterer in MST. Calculation results of a small array are shown to be in excellent agreement with measured data. Predictions and data show that perforated cylinders with empty cavities exhibit a strong and narrow insertion loss peak at resonance, though simultaneously suffer from amplification below resonance. By adding porous material in the core of the scatterer adverse effects below the resonance peak were suppressed. In addition, it was found that the reduction peak broadens, though at a cost of a reduced peak amplitude. Finally, it has been shown that adding porous material in a perforated shell will introduce partial absorption of the incoming field, which can be optimized by adjusting the perforation ratio of the shell.