The problem of impulsive interference modeling is considered. The proposed approach is based on the representation of the interference as the discontinuous Markov process observed at the output of the generally nonlinear filter, excited by a Poisson-distributed train of δ-pulses with random or constant energy. The dependence of the probability density and correlation functions of the simulating process on the filter structure and on the excitation characteristics is investigated. Examples of the considered model synthesis are included. The concept suggested should prove useful in simulators of the interference in continuous communication channels and in synthesis of optimal signal processing algorithms in the impulsive environment.