  Naturally occurring radionuclide $^{210}$Pb ($T_{1/2}$=22.2 y) is an
important source of background in rare event searches, such as neutrinoless
double-$\beta$ decay and dark matter direct detection experiments. When a
sample mass of hundreds of grams is available, $\gamma$-counting measurements
can be performed. However, there are other cases where only grams of sample can
be used. For these cases, better sensitivities are required.
  In this paper, in collaboration with the Astroparticle Physics group at
Carleton University, the capabilities of the A.E. Lalonde AMS Laboratory at the
University of Ottawa for $^{210}$Pb measurements are discussed. PbF$_{2}$ and
PbO targets were used, selecting in the low energy sector, respectively,
(PbF$_{3}$)$^{-}$ or (PbO$_{2}$)$^{-}$ ions.
  For fluoride targets, the blank $^{210}$Pb/$^{206}$Pb ratio was in the
10$^{-14}$ to 10$^{-13}$ range, but current output was lower and less stable.
For oxide targets, current output showed better stability, despite a
significant difference in current output for commercial PbO and processed
samples, and background studies suggested a background not much higher than
that of the fluoride targets. Both target materials showed, therefore, good
performance for $^{210}$Pb AMS assay.
  Measurements of Kapton films, an ultra-thin polymer material, where masses
available are typically just several grams, were performed. 90% C.L. upper
limits for the $^{210}$Pb specific activity in the range of 0.85-2.5 Bq/kg were
established for several Kapton HN films.
