Let X = {a} ${cup}$ {$a_{i}$ ${$mid$}$</TEX>i $in$ N} be a subspace of Euclidean space $E^2$ such that $lim_{{i}{longrightarrow}{$infty}}a_{i}$ = a and $a_{i};{ eq};a_{j}$ for $i{ eq}j$. Then it is well known that the space X has no expansive homeomorphisms with the shadowing property. In this paper we show that the set of all expansive homeomorphisms with the shadowing property on the space Y is dense in the space H(Y) of all homeomorphisms on Y, where Y = {a, b} ${cup}$ {$a_{i}{$mid$}i{in}Z$</TEX>} is a subspace of $E^2$ such that $lim_{i}$-$infty$ $a_{i}$ = b and $lim_{{i}{longrightarrow}{$infty}}a_{i}$</TEX> = a with the following properties; $a_{i}{ eq}a_{j}$ for $i{ eq}j$ and $a{ eq}b$.