The mean isophotal axis ratios are computed for a complete sample of 119 brightest cluster galaxies (BCGs) in Abell clusters. The cumulative distribution function F(q) of axis ratios for the BCGs differs from F(q) for a sample of ordinary elliptical galaxies at only the P=0.14 probability level, as measured by a Kolmogorov Smirnov test. In contrast, a sample of 30 s brightest cluster ellipticals has axis ratios which are significantly rounder (P K-S =0.01) than those of the BCGs. We model the distribution of intrinsic axis ratios f(β, γ) as an isotropic Gaussian in the space 0≤γ≤β≤1, where β and γ are the scaled lengths of the intermediate and shortest axes