We investigate femtosecond laser irradiation of dielectric materials containing randomly-arranged nanoparticles. For this, numerical modeling is performed based on three different methods: Mie theory, static solution of linear Maxwell's equations and a solution of nonlinear Maxwell's equations together with kinetic equations for free electron excitation/relaxation processes. First two approaches are used to define the static intensity distribution and to analyze the electromagnetic interaction between the nanoparticles. The third method allows us to investigate the complex dynamics of the laser-matter interaction. Multiphoton absorption is shown to be responsible for electron plasma generation in the regions of strong intensity enhancements in the vicinity of nanoparticles. The irradiation of the dielectric material leads to the elongation of nanoplasmas by the near-field enhancement perpendicular to the laser polarization and to their strong interaction resulting in periodic arrangement. Numerical results shed light on such effects as femtosecond laser-induced nanograting formation.