  We perform resummation of soft gluon corrections to the total cross section
for the process $pp \to t\bar{t}H$. The resummation is carried out at
next-to-leading-logarithmic (NLL) accuracy using the Mellin space technique,
extending its application to the class of $2 \to 3$ processes. We present an
analytical result for the soft anomalous dimension for a hadronic production of
two coloured massive particles in association with a colour singlet. We discuss
the impact of resummation on the numerical prediction for the associated Higgs
boson production with top quarks at the LHC.
