Viscoelastic models are necessary to simulate the behavior of time-dependency materials such as polymer industrial products and biological tissues. Indentation test have been widely used in the many study because of its simplicity for estimate of local mechanical properties of bulk materials. This study obtained analytical solution of relaxation indentation problem of viscoelastic thin layer bonded on rigid substrate indented by flat-ended cylindrical punch using elastic-viscoelastic corresponding principle for axisymmetric elastic contact problem. The relaxation indentation test is conducted for two different polymer materials which are polymethyl methacrylate (PMMA) and polyvinyl chloride (PVC) and bovine articular cartilage of the femoral head. For bovine articular cartilage, normal cartilage treated by collagenase after relaxation indentation test and test is conducted again. The standard linear solids model is chosen as viscoelastic model in this study, then viscoelastic parameters of the model are determined by fitting experimental data collected from the relaxation indentation test. As results, the values of Root Mean Squared Error (RMSE) which indicate the error between experimental data and analytical solution show 0.59, 0.37 for respectively PMMA, PVC and 0.78, 0.52 for respectively normal and treated bovine articular cartilage. The results indicate articular cartilage needs more complicated viscoelastic model than the standard linear solid model. The analysis provide a fundamental basis for evaluating viscoelastic parameters of thin layer with the relaxation indentation test.