We estimate the distribution of intrinsic shapes of UZC–SSRS2 groups of galaxies from the distribution of their apparent shapes. We measure the projected group axial ratio using the moments of their discrete galaxy distribution. Then, using the non-parametric kernel method to estimate the smooth apparent axial ratio distribution, we numerically invert a set of integral equations to recover the corresponding intrinsic distribution under the assumption that groups are either oblate or prolate spheroids. We find that the prolate spheroidal model fits very well the UZC–SSRS2 group distribution with a true mean axial ratio 〈β〉≃ 0.3 and σβ≃ 0.15. This shows that groups of galaxies are significantly more elongated, both on the plane of the sky and in three dimensions, than clusters of galaxies. The poorest groups that we consider, those with four members, are even more elongated than the overall population with 85 per cent of the groups having β≲ 0.4.