For a spheroidal heat flux meter appropriately oriented in an infinite volume of a medium in which there is a steady heat flux, f, the ratio of mean flux density through the meter to the flux density through the medium is related to ∈, the ratio of meter conductivity to medium conductivity, by an (exact) equation of the form f=∈1+(e-1)H with H a function of meter geometry only. For the oblate spheroid with η ( = length of minor axis/length of major axes) small, H = 1 - (π/2)η. It is argued that the equation should hold reasonably well for other meter shapes, and that, for thin meters, the relation H = 1 - αr, which yields f= 1/[1 - αr(l - ∈ −1)], should be valid to a good approximation, α is a constant and r is the ratio of mean meter thickness in the general direction of the heat flow to the square root of the mean cross section the meter presents normal to this direction. For the oblate spheroid α = 1.70. The assumption that meters of other shapes may be replaced for the purposes of analysis by a spheroid with the same r value is equivalent to applying the value α = 1.70 to all meter shapes. The analog solutions of Portman [1958] for the square plate meter yield α = 1.31 with a standard deviation of 0.59. It is shown that Portman's exponential equation and the present theory agree closely (though perhaps fortuitously) for ∈ close to or greater than 1; but the exponential equation is definitely incorrect at small ∈. This study indicates that the errors in heat flux meters are minimized if the following conditions are satisfied: (a) The meter is made as thin as possible. (b) The meter is calibrated in a medium with conductivity equal to the arithmetic mean of the extremes in which the meter is to be exposed (exact for small errors), (.c) The conductivity of the meter is made as great as possible, (c) suggests that meters which include a sheet of an insulating material such as Lucite or Bakelite may not be so suitable for exposure to the full range of soil conditions as are meters consisting almost entirely of metals. However, uncertainties about thermal contact probably set a very real limit to the accuracy of heat flux meters exposed in media such as soil.