We have solved a polymerizing version of the mean spherical approximation (MSA) for polyelectrolytes. The polyelectrolytes are modeled as tangentially bonded hard-sphere segments interacting via the Coulombic potential in a continuous medium with dielectric constant. Analytical solutions for thermodynamic properties and radial distribution functions at contact are obtained for some specific systems (negatively charged chains and counterions) studied in the literature via computer simulations, with which good agreement is found for the osmotic pressure.