  Let $F$ be a free group of finite rank. We say that the monomorphism problem
in $F$ is decidable if for any two elements $u$ and $v$ in $F$, there is an
algorithm that determines whether there exists a monomorphism of $F$ that sends
$u$ to $v$. In this paper we show that the monomorphism problem is decidable
and we provide an effective algorithm that solves the problem.
