The authors study theoretically the electrostatic equilibria for a shell filled with a suspension of polyions (e.g., colloids, polyelectrolytes, etc.) and immersed in an infinite salt-free reservoir. The shell is treated as impermeable for polyions, but allowing free diffusion of counterions. From the solution of the linearized Poisson-Boltzmann equation we obtain the distribution of the potential and concentration profiles for polyions. The authors then derive explicit formulas for the excess electro-osmotic pressure of a polyion solution exerted by the shell. This is shown to be due to a concentration of polyions at the inner shell boundary and can be very different from the pressure of a corresponding bulk polyion solution.