An effective route for the synthesis of aliphatic polyesters made from adipic or sebacic acid and alkanediols, using inorganic acid as a catalyst is reported. The monomer composition, reaction time, catalyst type, and reaction conditions were optimized to yield polyesters with weight average molecular weights of 23,000 for adipic acid and 85,000 for sebacic acid-based polyesters. The polymers melt at temperatures of 52–65°C and possess melt viscosity in the range of 5600–19,400cP. This route represents an alternative method for producing aliphatic polyesters for possible use in the preparation of degradable disposable medical supplies.