A mathematical model of diffraction of electromagnetic microwaves on explosive materials with different physical and electromagnetic parameters has been developed. The model was constructed by solving Maxwell's equation for two surfaces separating three dielectric materials, in particular air, explosive material, and the substrate on which the explosive material is located. Different types of soil and wood are considered as the substrate material, which meets the conditions for demining large areas of the locality. The results of the numerical calculation showed that 67 % to 92 % of the energy of electromagnetic radiation is concentrated in the explosive material. In this case, trinitrotoluene, which is placed on dry sand, has the highest absorption rates, while wet wood, due to its high coefficient of dielectric permittivity, successfully transmits electromagnetic microwaves through its surface. The obtained models and numerical results are considered as theoretical basis for predicting the effectiveness of remote methods of detection and disposal of explosive materials using electromagnetic microwaves. The obtained results showed that this method will be least effective for explosive materials placed on wet wood. In this case, the lowest reflection coefficient is observed that complicates the search for explosive material and the lowest absorption coefficient that complicates the artificial detonation of explosive material due to its heating under the influence of electromagnetic microwaves.