Currently, the terahertz-frequency range, which is on the border of the microwave and optical ranges, is being intensively utilized. One of the widely used materials in terahertz optics is indium antimonide (InSb), the plasma frequency of which depends on the degree of doping, temperature, and surface illumination. The possibility of generating surface plasmon polaritons, a type of surface electromagnetic waves, on the surface of an InSb sample using the attenuated-total-reflection method (ATR) (Otto scheme) is discussed. Using the scattering-matrix formalism, the conditions for the highest efficiency of the excitation of surface plasmon polaritons are established. If terahertz radiation with a frequency ω slightly less than ωp is used for this, the propagation length of such plasmons and the depth of their field penetration into the environment (air) are comparable to the radiation wavelength. It is possible to achieve surface plasmon resonance in the form of a sharp decrease in the intensity of monochromatic radiation reflected from the base of the ATR prism with a change in the angle of incidence and the size of the air gap. Test experiments were performed to observe the surface plasmon resonance on an InSb wafer using a high-resistance silicon prism and monochromatic radiation (λ = 141 μm) from the Novosibirsk free electron laser. The dependence of the resonant dip on the size of the air gap separating the prism from the sample surface is studied, and its optimal (in the case of resonance) value is established for semiconductors with a plasma frequency in the terahertz range.