In pursuit of research to create a synthetic tissue scaffold by a micropunching process, material properties of polycaprolactone (PCL) in liquid nitrogen were determined experimentally and used for finite element modeling of cryogenic micropunching process. Specimens were prepared using injection molding and tested under compression to determine the stress–strain relationship of PCL below its glass transition temperature. Cryogenic conditions were maintained by keeping the PCL specimens submerged in liquid nitrogen throughout the loading cycle. Specimens of two different aspect ratios were used for testing. Yield strength, strength coefficient, and strain hardening exponent were determined for different specimen aspect ratios and extrapolated for the case with zero diameter to length ratio. Material properties were also determined at room temperature and compared against results available in the literature. Results demonstrate that PCL behaves in a brittle manner at cryogenic temperatures with more than ten times increase in Young's modulus from its value at room temperature. The results were used to predict punching forces for the design of microscale hole punching dies and for validation of a microscale hole punching model that was created with a commercially available finite element software package, deform 3D. The three parameters, yield strength, strength coefficient, and strain hardening exponent, used in Ludwik's equation to model flow stress of PCL in deform 3D were determined to be 94.8 MPa, 210 MPa, and 0.54, respectively. The predicted peak punching force from finite element simulations matched with experimentally determined punching force results.