Thermoplastic polyurethane (TPU) belongs to the group of elastomers, which are characterized by high elasticity and resistance to mechanical loading. The combination of elastomeric properties with the capability to be processed using methods typical for thermoplastic materials. In this case, TPU makes an attractive alternative to typical materials used in injection molding processes. Due to its wide range of applications, TPU is used, among others, in the automotive, medical, and footwear industries, as well as in automation systems. This study aimed to determine the ultimate tensile stress value and the elastic deformation characteristics of TPU material subjected to uniaxial tensile loading. The specimens used in the study were prepared in accordance with the ISO 37:2017 standard, using the Fused Deposition Modeling (FDM) technique. Based on established methods and the obtained stress–strain curves, the following mechanical properties were determined: tensile strength, elongation at break, elasticity modulus, sum of strain energy, and yield strength. The results presented in this paper made it possible to determine the variation of ultimate tensile stress as a function of infill density.