  We estimate the distribution of intrinsic shapes of the APM galaxy clusters
from their corresponding distribution of projected shapes. We smooth the
discrete galaxy distribution and define the cluster shape by fitting the best
ellipse to the different isodensity contours. Using Monte-Carlo simulations we
have studied the performance of our method in the presence of the expected
galaxy background, at the different distances traced by the APM clusters, and
we have devised a method to correct statistically the projected cluster shapes
for discreteness effects and random fluctuations. We find that the true cluster
shape is consistent with that of prolate spheroids.
