The theoretical model of infrared point target detection system is systematically analyzed. The transmittance of medium-wave and long-wave infrared light under typical atmospheric conditions is calculated by establishing the atmospheric stratification model and combining the MODTRAN model. The comparison data of the two calculation results can provide reference for the band selection in the design of infrared detection system. By analyzing the theoretical model of infrared radiation intensity of targets, the infrared radiation intensity of several typical targets in different wavebands is calculated, which provides support for the demonstration of operation range for IR system. Based on the probability density distribution function of infrared image noise, the theoretical formulas of image signal-to-noise ratio, system detection probability and false alarm probability are derived, which provide reference for setting detection threshold. The theoretical model analysis results of infrared point target detection system''s operation range can offer an important theoretical support for improving the credibility of infrared detection system''s operation range demonstration and the rationality of system parameter design.