An idealized theory of flame propagation is formulated to explain the effects of tube diameter, mixture composition, and direction of motion in a gravity field on the flame shape and ``speed of uniform motion'' of a flame front propagating through a stationary air-fuel mixture contained in a long tube. The effect of local flame curvature on flame speed and viscous effects within the fluid are considered, for it is believed that both play major roles in the production of a steady flame of finite amplitude. Ideally it is possible to match the present theory (valid far from a real wall) to a theory that accounts for the flame shape of the ``quenched'' portion of the flame close to the wall. This matching is only discussed qualitatively.