  Double white dwarf binaries in the Galaxy dominate the gravitational wave sky
and would be detectable for an instrument such as LISA. Most studies have
calculated the expected gravitational wave signal under the assumption that the
binary white dwarf system can be represented by two point masses in orbit. We
discuss the accuracy of this approximation for real astrophysical systems. For
non-relativistic binaries in circular orbit the gravitational wave signal can
easily be calculated. We show that for these systems the point mass
approximation is completely justified when the individual stars are
axisymmetric irrespective of their size. We find that the signal obtained from
Smoothed-Particle Hydrodynamics simulations of tidally deformed, Roche-lobe
filling white dwarfs, including one case when an accretion disc is present, is
consistent with the point mass approximation. The difference is typically at
the level of one per cent or less in realistic cases, yielding small errors in
the inferred parameters of the binaries.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics;General Relativity and Quantum Cosmology