  We consider the model of i.i.d. first passage percolation on $\mathbb{Z}^d$ :
we associate with each edge $e$ of the graph a passage time $t(e)$ taking
values in $[0,+\infty]$, such that $\mathbb{P}[t(e)<+\infty] >p_c(d)$.
Equivalently, we consider a standard (finite) i.i.d. first passage percolation
model on a super-critical Bernoulli percolation performed independently. We
prove a weak shape theorem without any moment assumption. We also prove that
the corresponding time constant is positive if and only if
$\mathbb{P}[t(e)=0]<p_c(d)$.
