Physically Unclonable Functions (PUFs), as an alternative hardware-based security method, have been chal- lenged by some modeling attacks. As is known to all, samples are significant in modeling attacks on PUFs, and thus, some efforts have been made to expand sample sets therein to improve modeling attacks. A closer examination, however, reveals that not all samples contribute to modeling attacks equally. Therefore, in this article, we introduce the concept of sample essentiality for describing the contribution of a sample in model- ing attacks and point out that any sample without sample essentiality cannot enhance some modeling attacks on PUFs. As a by-product, we find theoretically and empirically that the samples expanded by the procedures proposed by Chatterjee et al. do not satisfy our sample essentiality. Furthermore, we propose the notion of essential sample sets for datasets and discuss its basic properties. Finally, we demonstrate that our results about sample essentiality can be used to reduce samples efficiently and benefit sample selection in modeling 42 attacks on arbiter PUFs.