Monte Carlo simulations of linear polyelectrolyte solutions containing mixed valency simple ions in the cylindrical cell model are reported. The equilibrium distributions of the simple ions and the osmotic pressure of the solution are calculated at various concentrations of the monomer units of the polyelectrolyte. Specifically, the following systems are studied - monovalent counterions with added 2:2 salt, divalent counterions with added 1:1 salt, and systems containing mono-and divalent counterions only, and mono-and trivalent counterions only. The simulation results are compared with the corresponding predictions from the Poisson-Boltzmann and modified Poisson-Boltzmann theories applied to the cell model. It is seen that upto moderate concentrations of the polyion, the modified Poisson-Boltzmann theory provides a very good description of the systems with deviations occurring at higher concentrations. The theory also reproduces the charge reversal observed in the simulations when strongly correlated counterions overscreen the charge of the polyion. On the other hand, the classical Poisson-Boltzmann results begin to show discrepencies from the Monte Carlo results at relatively lower concentrations. Comparisons of the simulated osmotic pressures with available experimental results confirm the validity of the cell model in a spectrum of practical situations of interest. (C) 1997 American Institute of Physics.