  We study the finite-size scaling properties of the Ising model on the Moebius
strip and the Klein bottle. The results are compared with those of the Ising
model under different boundary conditions, that is, the free, cylindrical, and
toroidal boundary conditions. The difference in the magnetization distribution
function $p(m)$ for various boundary conditions is discussed in terms of the
number of the percolating clusters and the cluster size. We also find
interesting aspect-ratio dependence of the value of the Binder parameter at
$T=T_c$ for various boundary conditions. We discuss the relation to the
finite-size correction calculations for the dimer statistics.
