Polyurethane foams which are highly flame resistant are described, as well as the production of such polyurethane foams by the reaction between a natural polyol, such as sucrose or a blend of mono- or disaccharides in place of the standard hydrocarbon-based polyol component, a polyisocyanate and water in the presence of a suitable polyurethane forming catalyst and a non-halogenated flame retardant, and optionally one or more components such as surfactants and/or emulsifiers. The resultant polyurethane foam has a bio-based solid content ranging from about 17% to 30%, may be formulated in a variety of foam densities for a variety of applications, and exhibits a high degree of fire and burn resistance, as exhibited by the flame spread index, flash over resistance determination, and the smoke spread values.