Observed in many real applications, a top-k query often consists of two components to reflect a user's preference: a selection condition and a ranking function. A user may not only propose ad hoc ranking functions, but also use different interesting subsets of the data. In many cases, a user may want to have a thorough study of the data by initiating a multi-dimensional analysis of the top-k query results. Previous work on top-k query processing mainly focuses on optimizing data access according to the ranking function only. The problem of efficient answering top-k queries with multidimensional selections has not been well addressed yet. This paper proposes a new computational model, called ranking cube, for efficient answering top-k queries with multidimensional selections. We define a rank-aware measure for the cube, capturing our goal of responding to multidimensional ranking analysis. Based on the ranking cube, an efficient query algorithm is developed which progressively retrieves data blocks until the top-k results are found. The curse of dimensionality is a well-known challenge for the data cube and we cope with this difficulty by introducing a new technique' of ranking fragments. Our experiments on Microsoft's SQL Server 2005 show that our proposed approaches have significant improvement over the previous Methods.