  We discuss production of $p\bar{p}$ pairs in two-photon interactions in
heavy-ion collisions. We present predictions for the ultraperipheral,
ultrarelativistic, heavy-ion collisions (UPC) $^{208}\!Pb \, ^{208}\!Pb \to$
$^{208}\!Pb \, ^{208}\!Pb \,p \bar{p}$. The parameters of vertex form factors
are adjusted to the Belle data for the $\gamma \gamma \to p \bar{p}$ reaction.
To described the Belle data we include the proton-exchange, the $f_2(1270)$ and
$f_2(1950)$ $s$-channel exchanges, as well as the hand-bag mechanism. Then, the
total cross section and several differential distributions for experimental
cuts corresponding to the LHC experiments are presented. The distribution in
$\mathrm{y}_{diff}$, the rapidity distance between the proton and antiproton,
is particularly interesting. We find the total cross sections: 100 $\mu$b for
the ALICE cuts, 160 $\mu$b for the ATLAS cuts, 500 $\mu$b for the CMS cuts, and
104 $\mu$b taking into account the LHCb cuts. This opens a possibility to study
the $\gamma \gamma \to p \bar{p}$ process in UPC at the LHC.
