  Let $\bbk$ be an algebraically closed field of prime characteristic $p$. If
$p$ does not divide $n$, irreducible modules over $\frak {sl}_n$ for regular
and subregular nilpotent representations have already known(see \cite{Jan2} and
\cite{Jan3}). In this article, we investigate the question when $p$ divides
$n$, and precisely describe simple modules of $\frak {sl}_n$ for regular and
subregular nilpotent representations.
