Novel PE- and PP-based electromagnetic wave shielding and absorbing materials with low combustibility, enhanced thermal and mechanical properties, containing graphite, grinded wood and fire retardants, were developed and investigated. Their flame-resistance, thermal and mechanical properties are investigated. Electromagnetic wave reflection coefficients of the materials over the frequency range 20-40 GHz were measured; despite low concentration (10%) of functional filler, reflection coefficient can be as low as -15 dB. Criteria of incombustibility of polymeric composites are formulated: thermochemical, kinetic, thermal, physical and mass transfer. These criteria allowed to set up the principles of decreasing combustibility of polymeric composites. Materials requirements, allowing to choose the most effective shielding and fireproof systems for multicomponent composites, containing polymers, wood and other fillers, were formulated.