The method for producing non-core beta silicon carbide fibers includes four steps. The first step is spinning of multifilament polymeric fiber by melt-extrusion of polycarbosilane. The second step is thermooxidative cross-linking for which the produced spun polymeric fibers are cured in an oxidation furnace at a temperature of 175-250 degrees C. at a heating rate of 3-10 degrees C./h until their weight is increased by 6-15%. The third step is carbonization of the produced cured polymeric fibers with the conversion into the ceramic phase. The fourth step is finishing of the produced beta silicon carbide fiber. The effect of the invention is producing non-core silicon carbide fibers, improving their strength performance, improving resistance to high temperatures and their high creep resistance, stable fiber properties, optimal average diameter of fibers, absence of foreign impurities in the fiber composition.