The Stirling number of the second kind (or Stirling partition number) which are denoted by \(S(n,k)\) have many applications in mathematics, and particularly in combinatorics. \(S(n,k)\) is the number of ways to partition a set of $n$ objects into \(k\) non-empty ones. Note that \(k!S(n,k)\) also has a combinatorial interpretation: it is the number of all surjections from a set with \(N\) elements onto a set with \(k\) elements. By using some basic facts about the field of \(p\)-adic numbers and \(p\)-adic locally analytic functions, the author has studied the \(p\)-adic valuations of Stirling numbers. He gives many results and comments on the $p$-adic valuations of Stirling numbers.