This paper presents a numerical study of the structural parameters of a one-dimensional chain of three dust particles levitating in the near-electrode layer of an rf discharge or in the stratum of a dc discharge. The model considers the motion of dust particles under the action of gravity, external electric field, the Coulomb repulsion, and the electrostatic force from the space charge surrounding the dust particles. Particular attention is paid to the effect of plasma polarization around dust particles and the wake formation under the action of the external electric field. Calculations showed that the charge of the first dust particle in the chain and the total charge of the entire chain, as well as the length of the chain, grow linearly with the external electric field strength. Obtained data are in qualitative agreement with the experimental and numerical data presented in the literature. It was shown that for a certain large value of the external electric field, the charge of the third dust particle is the smallest of all the particles in the chain. It was found that with an increase in the mean value of the external electric field, the chain of dust particles is displaced as a whole in the direction opposite to the action of the electrostatic force on them.