Additive manufacturing (AM) is a disruptive technology that enables one to manufacture complex structures reducing both time and manufacturing cost. Among the materials commonly used for AM, thermoplastic elastomers (TPE) are of high interest due to their energy absorption capacity, energy efficiency, cushion factor or damping capacity. Previous investigations have exclusively focused on the optimization of the printing parameters of commercial TPE filaments and the structures to analyse the mechanical properties of the 3D printed parts. In the present paper, the chemical, thermal and mechanical properties for a wide range of commercial thermoplastic polyurethanes (TPU) filaments were investigated. For this purpose, TGA, DSC, ¹H-NMR and filament tensile strength experiments were carried out in order to determine the materials characteristics. In addition, compression tests have been carried out to tailor the mechanical properties depending on the 3D printing parameters such as: infill density (10, 20, 50, 80 and 100%) and infill pattern (gyroid, honeycomb and grid). The compression tests were also employed to calculate the specific energy absorption (SEA) and specific damping capacity (SDC) of the materials in order to establish the role of the chemical composition and the geometrical characteristics (infill density and type of infill pattern) on the final properties of the printed part. As a result, optimal SEA and SDC performances were obtained for a honeycomb pattern at a 50% of infill density.