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The paper presents study of one of the examples of nonequilibrium plasmas—dielectric barrier discharge in atmospheric air—using kinetic particle‐in‐cell code VORPAL. It has been demonstrated that the use of state‐of‐the‐art methods for solution of the electrostatic problems and the concept of variable‐weight particles for reduction number of particles in dense plasma regions made simulations numerically efficient. Using the developed model the propagation of the cathode‐directed streamer driven by 4ns positive pulse has been analyzed in both 2D and 3D. The model reproduced all essential physical phenomena of the streamer propagation. The model has been validated via grid resolution study and study of the concept of variable‐weight particles.