Conditions required for incipient boiling in liquid metal heat pipes are examined. It is shown that the heat flux for boiling in heat pipes can be larger than that for pool boiling if thin capillary wicks are used with low frictional resistance to liquid flow in the axial direction. Methods for calculating the heat flux for incipient boiling in heat pipes are derived. Data on nucleation site radii and interface heat transfer coefficients, needed for heat flux calculations, are available. An upper limit of 3 to 7 µ is determined for the nucleation site radius in sodium heat pipes.