Several different hydrocolloids, such as starch, have been proposed as suitable base materials (matrices) for edible films in food packaging. Edible films from native and modified starch plasticized with glycerol were developed. Starches were obtained from dark cush-cush yam (Dioscorea trifida) and cassava (Manihot esculenta C.) from Venezuela, and chemically modified by cross-linking with sodium trimetaphosphate. The uniaxial tensile, microstructural and barrier properties of the films were then evaluated to determine their potential as a replacement for existing synthetic materials used in the food industry. The structure of the materials showed that the gelatinization process of cush-cush yam films was poorer than that of cassava. The glycerol–starch interaction (glycerol-amylose) was stronger in the films composed of modified starches and was more marked in cassava based films. All the films studied exhibited promising mechanical properties, with those derived from cush-cush yams showing the highest Young's modulus and resistivity values. Cassava based edible films and films derived from modified starch from both sources showed maximum flexibility, reinforcing the idea that the glycerol–starch interactions are stronger in these materials. Crosslinked films tended to be more permeable to water vapor due to their hydrophilic characteristics. The properties observed in these biodegradable materials highlight their potential as food packaging materials, thus enabling the replacement of synthetic materials that contaminate the environment.