Aggregate similarity search, also known as aggregate nearest-neighbor (Ann) query, finds many useful applications in spatial and multimedia databases. Given a group Q of M query objects, it retrieves from a database the objects most similar to Q, where the similarity is an aggregation (e.g., sum, max) of the distances between each retrieved object p and all the objects in Q. In this paper, we propose an added flexibility to the query definition, where the similarity is an aggregation over the distances between p and any subset of ϕM objects in Q for some support0<ϕ≤1. We call this new definition flexible aggregate similarity search and accordingly refer to a query as a flexible aggregate nearest-neighbor (Fann) query. We present algorithms for answering Fann queries exactly and approximately. Our approximation algorithms are especially appealing, which are simple, highly efficient, and work well in both low and high dimensions. They also return near-optimal answers with guaranteed constant-factor approximations in any dimensions. Extensive experiments on large real and synthetic datasets from 2 to 74 dimensions have demonstrated their superior efficiency and high quality.