Although confined masonry and reinforced masonry construction have had good behavior in strong earthquakes occurred during the last decade, but the unreinforced masonry construction has had poor safety performance records during the past earthquakes. In view of this, a friction base isolation (FBI), system for multistory masonry building is considered here in which a clear smoothened surface is created between the superstructure and the sliding substructure. The earthquake response of the multistory masonry buildings with a FBI system subjected to the Koyna and El Centro earthquake ground motions is computed through a multi- mass-spring-dashpot mathematical model. The parameters involved in the seismic analysis are the number of stories of the building, the coefficient of friction and the type of earthquakes. The results are presented through graphs in terms of non-dimensional lateral force coefficient and drift to story height ratio plotted against the number of stories for different coefficients of friction and earthquakes. These plots show the reduction in response of the base isolated multistory masonry buildings compared with corresponding conventional buildings.