Temporomandibular joint (TMJ) disorders (TMDs) are not well understood and the mechanical differences between the regions of the mandibular condylar cartilage (MCC) and the TMJ disc have not been thoroughly compared. As of now, there are no commercially available regenerative therapies for the TMJ. Elucidating the mechanical properties of these two structures of the articulating joint will help future efforts in developing tissue engineering treatments of the TMJ. In this study, we evaluate the compressive properties of the porcine disc and mandibular condylar cartilage by performing unconfined compression at 10% strain with 4.5%/min strain rate. Punches (4 mm biopsy) from both tissues were taken from five different regions of both the MCC and TMJ: anterior, posterior, lateral, medial, and central. Previously, theoretical models of compression in the porcine tissue did not fit the whole ramp-relaxation behavior. Thus, the data stress–relaxation was fitted to the biphasic transversely isotropic model, for both the TMJ disc and cartilage. From the results found in the disc, it was found that the posterior region had the highest values in multiple viscoelastic parameters when compared to the other regions. The mandibular condylar cartilage was only found to be significantly different in the transverse modulus between the posterior and lateral regions. Both the TMJ disc and MCC had similar magnitudes of values (for the modulus and other corresponding compressive properties) and behavior under this testing modality.