Among novel scaffold fabrication techniques, 3D fiber deposition (3DF) has recently emerged as a means to fabricate well-defined and custom-made scaffolds for tissue regeneration, with 100% interconnected pores. The mechanical behavior of these constructs is dependent not only on different three-dimensional architectural and geometric features, but also on the intrinsic chemical properties of the material used. These affect the mechanics of the solid material and eventually of 3D porous constructs derived from them. For instance, poly(ethylene oxide terephthalate)-poly(butylene terephthalate) (PEOT/PBT) block copolymers are known to have mechanical properties, depending on the PEOT/PBT weight ratio in block form and on the molecular weight of the initial poly(ethylene glycol) (PEG) blocks. These differences are enhanced even more by their different swelling properties in aqueous media. Therefore, this article examines the influence of copolymer compositions in terms of their swelling on dynamic mechanical properties of solid material and porous 3DF scaffolds. The molecular weight of the starting PEG blocks used in the copolymer synthesis varied from 300 to 1000 g/mol. The PEOT/PBT weight ratio in the blocks used varied from 55/45 to 80/20. This corresponded to an increase of the swelling ratio Q from 1.06 to 2.46, and of the mesh size xi from approximately 9 Angstrom to approximately 47 Angstrom. With increased swelling, dynamic mechanical analysis (DMA) revealed a decrease in elastic response and an increase of viscoelasticity. Thus, by coupling structural and chemical characteristics, the viscoelastic properties of PEOT/PBT 3DF scaffolds may be fine tuned to achieve mechanical requirements for a variety of engineered tissues. Ultimately, the combination of 3DF and DMA may be useful to validate the hypothesis that mimicking the biomechanical behavior of a specific tissue for its optimal replacement is an important issue for at least some tissue-engineering applications.