Effective insulation of buildings and other industrial objects requires the use of materials and system solutions that ensure maximum uniformity and density of insulation shells. The study focuses on the development of insulation systems based on expanded polyethylene and, in particular, on the development of modified polyethylene with reduced flammability containing a flame-retardant modified montmorillonite clay, which does not hinder gas formation, and silicate nanofillers in layered construction. Active experiments based on mathematical design methods allowed us to establish an analytical relationship between flame-retardant and modifier consumption and extruder pressure and response functions: average density of polyethylene foam and flammability criterion. The flammability criterion was taken as the oxygen index of the modified polyethylene foam. A foaming agent masterbatch was used as the flame retardant. Analytical optimization of mathematical models obtained as a result of active experiments allowed us to determine the optimal flame-retardant consumption, which was 3.7-3.8% of the polymer mass. Optimised systems for average density and oxygen index of flammability of modified polyethylene were obtained. A nomogram for predicting the material properties and selecting the composition, and an algorithm for a computer program for evaluating the properties of modified polyethylene foam as a function of the values of various factors, were developed. Taking into account the possible expansion of the scope of application of rolled polyethylene foam and seamless insulation shells based on it, possible solutions for insulation systems were studied using the program THERM, and a combined insulation system was adopted.