The study deals with the Payne effect (a substantial decrease in the storage modulus of a particle-reinforced elastomer with an increase in the amplitude of mechanical oscillations). The influence of temperature, concentration of filler and amplitude and frequency of strains is analyzed on the mechanical response of filled rubbery polymers. Constitutive equations are derived using the concept of two interpenetrating networks: one comprises semiflexible polymeric chains connected to temporary junctions, whereas the other is formed by filler clusters. Adjustable parameters are found by fitting experimental data for natural rubber, bromobutyl rubber and styrene-butadiene rubber reinforced by carbon black and polymeric particles. The critical concentration of particles is determined that characterizes transition from an ensemble of disjoint clusters to the network of filler. The volume fraction of filler corresponding to this transition is found to be close to the theoretical predictions based on the percolation theory, as well as to experimental data for isolator-conductor transition.