Abstract: Foam bodies made of thermoplastic polyesters with high homogeneity, a low open-cell factor and high elongation at break under shear stress, the polyester foam containing at least one thermoplastic elastomer such as a thermoplastic copolyester elastomer, in quantities of, for example, 0.5 to 15% by weight based on the weight of the foam body. The foam bodies can be obtained by foaming a starting polyester with low intrinsic viscosity in a mixture with a modification means in the form of a premix containing dianhydrides of tetracarboxylic acids and thermoplastic copolyester elastomers.