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The Standard Model problems lead to the new theories of extra dimensions:Randall-Sundrum model, Arkani-Hamed-Dimopoulos-Dvali model and TeV$^{-1}$model. In the framework of these models with the help of computer programPythia8.2 were calculated the production cross sections for Kaluza-Kleinparticles at various energies at the LHC. The generation of monojet events fromscalar graviton emission was considered for number of extra dimensions, n=2, 4,6, for the energy at the LHC 14 TeV. Also are studied the graviton productionprocesses through the gluon-gluon, quark-gluon and quark-quark fusion processesand found some periodicity in the behavior of the graviton mass spectrum.Within Randall-Sundrum scenario were calculated $\sigma\times$ Br forproduction process of massive graviton, gg $\rightarrow$ $G^{*}$, and the mostprobable processes of graviton decay at 13 TeV, 14 TeV and 100 TeV.

Computer modeling of properties of Kaluza-Klein particles and their searches at the LHC