We study the size and shape of low-density regions in the local Universe, which we identify in the smoothed density field of the PSCz flux-limited IRAS galaxy catalogue. After quantifying the systematic biases that enter the detection of voids using our data set and method, we identify, using a smoothing length of 5 h−1 Mpc, 14 voids within 80 h−1 Mpc (having volumes ⩾103h−3 Mpc3) and, using a smoothing length of 10 h−1 Mpc, eight voids within 130 h−1 Mpc (having volumes ⩾8×103 h−3 Mpc3). We study the void size distribution and morphologies and find that there is roughly an equal number of prolate and oblate-like spheroidal voids. We compare the measured PSCz void shape and size distributions with those expected in six different cold dark matter (CDM) models and find that only the size distribution can discriminate between models. The models preferred by the PSCz data are those with intermediate values of σ8(≃0.83), independent of cosmology.