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We study a function field version of a classical problem concerning square-free values of polynomials evaluated at primes. We show that for a square-free polynomial   $f\in {\mathbb {F}_q}[t][x]$  , there is a limiting density as   $n\to \infty$   of primes   $P \in {\mathbb {F}_q}[t]$   of degree   $n$   such that   $f(P)$   is square-free.

SQUARE-FREE VALUES OF POLYNOMIALS EVALUATED AT PRIMES OVER A FUNCTION FIELD