  An attempt to study the feasibility of a new experiment to search for double
beta decay in $^{112}$Sn and $^{124}$Sn was carried out by using ultra-low
background HPGe detector (244 cm$^{3}$) inside the Gran Sasso National
Laboratory (LNGS) of the INFN (Italy). A small sample of natural Sn was
examined for 2367.5 h. The radioactive contamination of the sample has been
estimated. The data has also been considered to calculate the present
sensitivity for the proposed search; half-life limits $\sim$ $10^{17} -
10^{18}$ years for $\beta^{+}$EC and EC-EC processes in $^{112}$Sn and $\sim$
$10^{18}$ years for $\beta^{-}\beta^{-}$ transition in $^{124}$Sn were
measured. In the last section of the paper the enhancement of the sensitivity
for a proposed experiment with larger mass to reach theoretically estimated
values of half-lives is discussed.
