Hydrolytically degradable polymers in the form of biodegradable disposable medical devices for use in medicine and laboratories such as syringes, test tubes, catheters, tubing, trays, medical fabrics, and gloves are described. The devices are formed in whole or in part of a hydrolytically degradable polymer. In the preferred embodiment, the devices or structural components thereof degrade in a period of weeks to months, preferably within a year and more preferably within six months of exposure to aqueous solutions. Conventional hydrolytically degradable polymers may be utilized or these may be modified to increase mechanical or processing characteristics, for example, using a polyfunctional branching agent and/or a chain extending agent. In one embodiment, the hydrolytically degradable polymer is a member of a new class of polyesters comprising an aliphatic dicarboxylic acid, an aliphatic diol and optionally, one or more bifunctional fatty acids such as ricinoleic acid and/or castor oil. The devices are prepared using standard techniques, such as by injection molding, extrusion or melt spinning. The devices can be formed entirely of the degradable polymer, or they can be coated with a polymer coating in order to increase the compatibility of and reduce the possibility for interaction between the surface of the device and liquids that may come in contact with the device, or they may include core or other internal structural member formed of either the biodegradable or non-biodegradable material.