Additive manufacturing provides a rapid manufacturing method for a variety of materials with different applications. Thermoplastic Polyurethane (TPU) is a soft polymer material that can be 3D printed. In this work, we explore the mechanical properties of a 3D printed grid pattern structure with TPU. By changing the pattern’s cell size and wall thickness parameters, we control the density of the grid lattice and, as a result, the bulk elastic modulus of the structure. We compare simulation and physical compression tests and conclude that the bulk elastic modulus of a print is related to the infill percentage according to a cubic relationship, with higher infill percentage samples resulting in higher elastic moduli. The precise cell size and wall thickness parameter values are minor influences comparatively. The elastic moduli of the resulting samples span from 0.36 MPa with 23.44% infill to 21.83 MPa with 75% infill, compared to an elastic modulus of 64.31 MPa when printing at 100% density. We also explore other factors such as the sample size, the printer, the build orientation, and the sample geometry. The results have uses in a variety of applications, including a custom linear spring, a bistable gripper, or a soft robot finger.