A method of producing liquid polymeric polyols from epoxidized plant oils by ring-opening polymerization in an organic solvent in the presence of a catalyst to yield the desired polyols at room temperature. The properties of the polymeric polyols depend on the type of plant oil used as starting material. Typically, polymeric content of the purified plant oil based polyols ranges from 65% to 90%. The hydroxyl value and the acid value ranges from 30 to 90 mg KOH/g sample and 1 to 14 mg KOH/g sample respectively. The average molecular weight Mn ranges from 800 Da to 16000 Da. The liquid plant oil based polymeric polyols are reacted with excess diisocyanate to produce isocyanate terminated prepolymer. Subsequently, the prepared prepolymer is reacted with diol or diamine to polyurethane and polyurea respectively.