Let I\subset K[x,y] be a <x,y>-primary monomial ideal where K is a field.
This paper produces an algorithm for computing the Ratliff-Rush closure I for
the ideal I=<m_0,...,m_{n}> whenever m_{i} is contained in the integral closure
of the ideal <x^{a_{n}},y^{b_0}>. This generalizes of the work of Crispin
\cite{Cri}. Also, it provides generalizations and answers for some questions
given in \cite{HJLS}, and enables us to construct infinite families of
Ratliff-Rush ideals.