  A model of space-time foam, made by $N$ wormholes is considered. The Casimir
energy leading to such a model is computed by means of the phase shift method
which is in agreement with the variational approach used in Refs.[9-14]. The
collection of Schwarzschild and Reissner-Nordstr\"{o}m wormholes are separately
considered to represent the foam. The Casimir energy shows that the
Reissner-Nordstr\"{o}m wormholes cannot be used to represent the foam.
