  We use a microscopic multicluster model to investigate the structure of
$^{10}$Be and of $^{11}$Be. These nuclei are described by $\alpha+\alpha+n+n$
and $\alpha+\alpha+n+n+n$ configurations, respectively, within the Generator
Coordinate Method (GCM). The 4- and 5-body models raise the problem of a large
number of generator coordinates (6 for $^{10}$Be and 9 for $^{11}$Be), which
requires specific treatment. We address this issue by using the Stochastic
Variational Method (SVM), which is based on an optimal choice of the basis
functions, generated randomly. The model provides good energy spectra for
low-lying states of both nuclei. We also compute rms radii and densities, as
well as electromagnetic transition probabilities. We analyze the structure of
$^{10}$Be and of $^{11}$Be by considering energy curves, where one of the
generator coordinates is fixed during the minimization procedure.
