Momentum and energy integral analysis of planar and axisymmetric laminar, buoyant diffusion flames is presented with the objective of describing the flame properties and ambient air entrainment. The analysis follows the traditional momentum/energy integral technique utilizing the Howarth-Dorodnitzyn transformation for variable density flows and description of the velocity profiles through the flame region in the transformed constant-density coordinate system. The assumptions utilized in the formulation include the boundary layer and thin-flame approximations, a Prandtl and Schmidt number of unity and the product of molecular diffusivity-density squared being constant throughout the field. It is shown that a similarity solution exists for a vertical planar flame formed between a semi-infinite region of fuel in contact with a semi-infinite region of oxidizer and the results are presented in non-dimensional form in this case and are compared with their asymptotic values. For the steady laminar axisymmetric buoyant diffusion flames originating from circular burners, numerical solutions are obtained for different diameter burners. It is found that ambient air entrainment is predominantly determined by the air consumption at the flame front and only an additional small portion of mass (about 5% of that consumed at the flame front) is induced in the flame region. When compared with the measured air entrainment in buoyant diffusion flames, the computed entrainment rates are found to be significantly smaller than the experimental values. This points to the fact that unsteady large-scale engulfment of ambient air into fire plumes dominates over the diffusive and buoyant boundary-layer transport of air around a fire plume.