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Let $\bbk$ be an algebraically closed field of prime characteristic $p$. If$p$ does not divide $n$, irreducible modules over $\frak {sl}_n$ for regularand 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 andsubregular nilpotent representations.

Irreducible modules of $\frak {sl}_{mp}$ in characteristic $p$ with regular or subregular nilpotent $p$-character