The Higgs boson production in association with top and antitop quarks probes directly the top Yukawa coupling. Precise measurements of this channel cross section will be possible in the high luminosity mode of the LHC at 13~and 14~TeV. The current uncertainty of theory predictions is mostly due to theoretical uncertainty of the QCD correction. In this talk, improvements of the fixed order QCD calculations will be discussed due to all order soft gluon resummations at the NLL and NNLL accuracy. The results will be presented for differential and total cross section. As the calculations involve a novel application of the soft gluon resummation technique to a $2\to 3$ process with two colored particles in the final state, some aspects of this generalization will be discussed.