An analysis was made of stable, laminar, free convection, film boiling from isothermal vertical plates and horizontal cylinders surrounded by a saturated liquid, where radiation was only of minor importance. The mathematical techniques of boundary layer theory were used and the boundary layer equations were reduced to ordinary differential equations by means of a transformation similar to those used in free convection and condensation. The equations were solved for: (1) compressible flow with variable specific heat, (2) variable specific heat and density variations considered only in the evaluation of the buoyant force, and (3) the case of constant properties. Numerical results were obtained for: (1) near critical water at 2800 and 3100 psia with wall to liquid temperature differences of 250, 500, and 1000 deg F; (2) for fluids with Prandtl numbers of 2/3, 1, and 2; and (3) for mercury and methanol film boiling at one atmosphere, considering constant properties. The results obtained by assuming constant properties were compared to: (1) the results obtained by considering variable properties, (2) experimental results, and (3) the comparable case of laminar film condensation. It was shown that the method of considering density variations only in the evaluation of the buoyant force is not valid in film boiling. It was also shown that the constant property solutions for heat transfer did not always agree with solutions obtained considering compressible flow and variable specific heat. An approximate analysis of a non-isothermal wall, including the effects of radiation, was presented. It was shown that for high emissivity walls at high temperature, radiation is the controlling factor in film boiling heat transfer.