  Finite size effects in Euclidean ${\rm CP}^{N-1}$ models with periodic
boundary conditions are investigated by means of the $1/N$ expansion and by
Monte Carlo simulations. Analytic and numerical results for magnetic
susceptibility and correlation length are compared and found to agree for small
volumes. For large volumes a discrepancy is found and explained as an effect of
the physical bound state extension. The leading order finite size effects on
the Abelian string tension are computed and compared with simulations finding
agreement. Finite size dependence of topological quantities is also discussed.
