This invention relates to fire-resistant, flexible, molded, medium density polyurethane foams. These foams typically have a density of from 10 to 30 pcf. The foams are the reaction product of a) at least one polyester polyol, b) at least one highly branched polyether polyol, c) at least one chain extender, d) a polymethylene poly(phenyl isocyanate), an isocyanate group containing prepolymer based on a polymethylene poly(phenyl isocyanate), or mixtures thereof, e) a solid flame retardant and f) water. This invention also relates to a process for preparing these polyurethane foams in open molds.