This study investigates the overall and local response of porous media composed of a perfectly plastic matrix weakened by stress-free voids. Attention is focused on the specific role played by porosity fluctuations inside a representative volume element. To this end, numerical simulations using the Fast Fourier Transform (FFT) are performed on different classes of microstructure corresponding to different spatial distributions of voids. Three types of microstructures are investigated:​ random microstructures with no void clustering, microstructures with a connected cluster of voids and microstructures with disconnected void clusters. These numerical simulations show that the porosity fluctuations can have a strong effect on the overall yield surface of porous materials. Random microstructures without clusters and microstructures with a connected cluster are the hardest and the softest configurations, respectively, whereas microstructures with disconnected clusters lead to intermediate responses. At a more local scale, the salient feature of the fields is the tendency for the strain fields to concentrate in specific bands. Finally, an image analysis tool is proposed for the statistical characterization of the porosity distribution. It relies on the distribution of the ‘distance function’, the width of which increases when clusters are present. An additional connectedness analysis allows us to discriminate between clustered microstructures.