The temporomandibular joint (TMJ) disc is a central element in several TMJ disorders. Tissue-engineered TMJ disc replacements may alleviate discomfort associated with TMJ disorders;​ however, prior to developing a replacement, a thorough understanding of the native disc must be attained. Toward this end, we developed an unconfined compression, incremental stress relaxation viscoelastic model which simultaneously incorporates the strain increment magnitude and total deformation in the stress relaxation solution. This multiple strain step model was fit to stress relaxation data from (i) 80 test sites from eight porcine TMJ discs for the purposes of a surface–regional characterization and (ii) 30 test sites from five porcine TMJ discs for the purposes of a freeze–thaw characterization. The model estimated viscoelastic parameters accurately and surface–regional variations were detected throughout the TMJ disc. Regionally, the medial and anterior regions have the largest relaxation moduli, and the posterior and anterior regions have the largest instantaneous moduli. The inferior surface was found to have higher instantaneous modulus values than the superior surface. Furthermore, material properties were retained over five freeze–thaw cycles. The results of this study allow for the creation of design and validation criteria for future engineering efforts and shed light on the disc’s role in TMJ function and dysfunction.