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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 $t(e)$ takingvalues in $[0,+\infty]$, such that $\mathbb{P}[t(e)<+\infty] >p_c(d)$.Equivalently, we consider a standard (finite) i.i.d. first passage percolationmodel on a super-critical Bernoulli percolation performed independently. Weprove a weak shape theorem without any moment assumption. We also prove thatthe corresponding time constant is positive if and only if$\mathbb{P}[t(e)=0]<p_c(d)$.

Weak shape theorem in first passage percolation with infinite passage times