**I. Brevik**

*Division of Applied Mechanics**Norwegian University of Science and Technology**N-7491 Trondheim, Norway*

How to calculate the lowest-frequency contribution to the Casimir force between metallic surfaces is a delicate point. The problem is whether the zero Matsubara frequency (*m*=0) contributes to the transverse electric (TE) mode or not. By adopting the Drude dispersive model at low frequencies we show, by means of a limiting procedure, that the contribution from the*m*=0 TE mode has to be zero. Analytical work on the Casimir force is reported, both for spherical and for planar surfaces. Numerical results are given for planar surfaces, choosing gold as an example. Apparent theoretical difficulties coming from negative Casimir entropies in a restricted temperature interval are discussed. The present paper reports work done in collaboration with J. S. Høye, J. B. Aarseth, and K. A. Milton.