The indoor dose due to the radiation of ceramic and granite tiles, marble, granite and travertine plates, as well as some components of covering materials, produced in Serbia or imported from other countries, was estimated in the work. Activity concentrations of 226Ra, 232Th, and 40K were measured by the standard gamma-spectrometry system. The lowest content of the radionuclides was found in white marble (ARa = 2 Bq/kg, ATh < 2 Bq/kg, and AK < 3 Bq/kg), while the highest activities were in some granite samples (Balmoral red: ARa = 200 Bq/kg, ATh = 378 Bq/kg, and AK = 1679, and Madura Gold: ARa = 273 Bq/kg, ATh = 20 Bq/kg, and AK = 1456 Bq/kg). The indoor absorbed dose rate in air due to the gamma radiation from covering materials was determined based on the specific absorbed dose rate computed in this work. Concentration of 222Rn that emanated into the indoor space was also calculated from the known 226Ra content. The radiation hazard estimated from the usage of each sample was expressed through the evaluated effective dose. Almost all samples, except one, fulfil the dosimetric criterion for safe use.