We present the results of molecular dynamics simulations of polyelectrolyte solutions in near-Theta-conditions for polymer backbone. Polyelectrolyte solutions are modeled as an ensemble of bead-spring chains of charged Lennard-Jones particles with explicit counterions. Simulations were performed for both fully and partially charged polyelectrolyte chains with the number of monomers N varying from 25 to 300 in the range of polymer concentrations covering both dilute and semidilute regime. Polyelectrolyte chains in dilute solutions are nonuniformly stretched with the projection of the linear monomer density onto the end-to-end vector increasing logarithmically from the middle of the chain. The simulation results for chain size dependence on the degree of polymerization at different polymer concentrations are in good qualitative agreement with predictions of the modified scaling model that takes into account nonuniform stretching of polyelectrolyte chains. In semidilute solutions we confirm that the correlation length is inversely proportional to the square root of polymer concentration. By measuring the bond angle correlation function, we have determined that polyelectrolyte chains can be viewed as flexible chains with the persistence length proportional to the correlation length. Our results for the concentration dependence of chain size Re on polymer concentration for the longest chains (N = 187 and N = 300) are approaching the power law c(-1/4), predicted by the scaling model of salt-free polyelectrolyte solutions.