Defect formation in the samples of graphene, graphene oxide and silicon irradiated with Ar cluster and highly-charged ion irradiations were studied. Ar cluster ions, with acceleration energy E = 30 kV (Exogenesis nAccel00, Boston, USA) and total Ar cluster ion fluences ranged from 1x109 cm-2 to 1x1013 cm-2 were directed toward various surfaces. Highly-charged ions (HCI) bombardment on surfaces with highly charged Xeq+ (q = 22) was employed at Eurasian National University, Kazakhstan, using a DC-60 cyclotron accelerator. Multi-layer graphene oxide, single-layer graphene- (SLG), few-layer of graphene (FLG) and polished Si are used for irradiation experiments. The study of irradiated samples was conducted by Raman spectroscopy, atomic force microscopy (AFM). Uniformly distributed defects and craters were observed on the surfaces of graphene, graphene oxide and silicon irradiated with cluster and HCI beams in our experiments. Ab-initio density-functional theory (DFT) was used to study point defects and molecular-dynamics (MD) simulations were used for studying formation of craters due to gas cluster ion impacts in graphene. The results of simulations were compared with experimental craters and surface shape.