The work is devoted to the development of a mathematical model of the foam material of the filtering half mask. The analysis of the methods used to study the leveling of the negative effect of the compression pressure of the filtering half-mask on the soft tissues of the human face under conditions of long-term operation was carried out. In order to study the mutual influence in the medium "filter material - foam material - human soft tissues", it is proposed to conduct virtual tests using numerical methods. The development of mathematical models of linear viscoelastic materials is based on the study of the relationship between the input and output characteristics of viscoelastic materials: stress and strain. The paper is devoted to the development of the mathematical model of linear viscoelastic materials using a transfer function. The model is designed to investigate the relationship between stress and deformation in viscoelastic materials using numerical methods.