Let I\subset K[x,y] be a -primary monomial ideal where K is a field. This paper produces an algorithm for computing the Ratliff-Rush closure I for the ideal I= whenever m_{i} is contained in the integral closure of the ideal . 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.
