We estimate the stable rank of crossed products by
actions of the additive  semigroups of natural numbers 
under certain conditions on actions.
As an application we  estimate the stable rank of
canonical subalgebras of 
the Hecke $C^*$-algebra of Bost and Connes, which is isomorphic to
the  crossed product by the multiplicative semigroup 
of natural numbers of Laca and Raeburn, and 
also  estimate
that of the  crossed products by the additive 
semigroups of natural numbers of Larsen and Raeburn.