The concept of city-size distribution has riveted the attention of social scientists during the last four decades. The existence of three types of city-size distribution has been noted in the literature on city-size distribution and settlement system. These are central place, rank-size and primate city distributions. This paper is primarily concerned with the last two. The Rank-Size rule is one of the methods of analyzing total settlement network in a region and also a tool for analyzing the settlement system that helps in the description and interpretation of the relationship between rank and population size of urban centres. A city-size distribution, in which the largest, city is several times larger than the second largest is known as the primate city-size distribution. The present study aims to examine the validity of Rank-Size Rule in India’s backward region Eastern Uttar Pradesh. A Stochastic model of the actual and expected population of the primate city and its variation from the estimated one provides interesting results that the urban centres in Eastern U.P. do not completely conform to the rank size rule