Despite advances in biomaterials research, there is no ideal device for replacing weight-bearing soft tissues like menisci or intervertebral discs due to poor integration with tissues and mechanical property mismatch. Designing an implant with a soft and porous tissue-contacting structure using a material conducive to cell attachment and growth could potentially address these limitations. Polycarbonate urethane (PCU) is a soft and tough biocompatible material that can be 3D printed into porous structures with controlled pore sizes. Porous biomaterials of appropriate chemistries can support cell proliferation and tissue ingrowth, but their optimal design parameters remain unclear. To investigate this, porous PCU structures were 3D-printed in a crosshatch pattern with a range of in-plane pore sizes (0 to 800 μm) forming fully interconnected porous networks. Printed porous structures had ultimate tensile strengths ranging from 1.9 to 11.6 MPa, strains to failure ranging from 300 to 486%, Young's moduli ranging from 0.85 to 12.42 MPa, and porosity ranging from 13 to 71%. These porous networks can be loaded with hydrogels, such as collagen gels, to provide additional biological support for cells. Bare PCU structures and collagenhydrogel-filled porous PCU support robust NIH/3T3 fibroblast cell line proliferation over 14 days for all pore sizes. Results highlight PCU's potential in the development of tissue-integrating medical implants.