We study the effect of an anomalously strong interaction of electromagnetic radiation with very thin conducting fibers. Metal, semiconductor or graphite fibers, which diameter is several hundred times smaller than the radiation wavelength, strongly absorb and scatter the electromagnetic waves, which electric vector is parallel to the fiber axis. The efficiency factors of attenuation, absorption, scattering and pressure of radiation for fibers with a diameter of several micrometers in the centimeter and millimeter ranges reach several thousand. We determine the nature of this effect. It occurs when the transverse dimension of the fiber is comparable to the thickness of the skin layer. Then the electric field of the incident wave fills the entire volume of the fiber, and the absorbed power is the highest. We also provide a theoretical analysis of such effect, determine conditions for its existence: the ratio between the radiation wavelength and the diameter of the fiber, the value of conductivity. We also provide an experimental study of the effect, when unfocused radiation beam with a wavelength of 8 mm at the output of waveguide with a 7.2 3.4 mm cross section transfers more than 10% of the beam power to a 12 μm diameter graphite fiber. We make an analysis of the mathematical model of the process of heating of graphite fiber by a microwave radiation beam. Then we solve a heat conduction equation and find the temperature distribution along the fiber, which is in agreement with the measured one.