We estimate the distribution of intrinsic shapes of APM galaxy clusters from
the distribution of their apparent shapes. We measure the projected cluster
ellipticities using two alternative methods. The first method is based on
moments of the discrete galaxy distribution while the second is based on
moments of the smoothed galaxy distribution. We study the performance of both
methods using Monte Carlo cluster simulations covering the range of APM cluster
distances and including a random distribution of background galaxies. We find
that the first method suffers from severe systematic biases, whereas the second
is more reliable. After excluding clusters dominated by substructure and
quantifying the systematic biases in our estimated shape parameters, we recover
a corrected distribution of projected ellipticities. We use the non-parametric
kernel method to estimate the smooth apparent ellipticity distribution, and
numerically invert a set of integral equations to recover the corresponding
distribution of intrinsic ellipticities under the assumption that the clusters
are either oblate or prolate spheroids. The prolate spheroidal model fits the
APM cluster data best.Comment: 8 pages, including 7 figures, accepted for publication in MNRA