  We calculate the Casimir energies due to matter fields with various boundary
conditions along two compact directions in $T^{2}$ compactification. We discuss
whether the Casimir energies generate attractive or repulsive forces. On the
theories with extra dimensions, the Casimir energy plays a crucial role in the
mechanism for stabilizing the size of extra dimensions. Finally we argue a
procedure of the application to $Z_{2}$ orbifold.
