This study intends to evaluate the ratcheting response of biological samples prepared from bovine and porcine trabecular bone, articular cartilage, meniscus, and skin tissues and tested under asymmetric (nonzero mean stress) cycles. Meniscus and skin samples were tested with stress ratios of R=0.1 and R=0.6, respectively, while other tissues were tested at R=0. Experimental ratcheting data and related influential parameters including stress level, stress rate, and testing frequency were discussed. A parametric ratcheting equation was further calibrated to estimate the ratcheting response of tissues. The predicted ratcheting data were found to be in close agreement with the reported experimental data.