Rheological constitutive relations for the apple cortex tissue have been developed by studying the creep behavior under both shear and hydrostatic loading conditions. Creep behavior in shear was studied by subjecting cylindrical samples to various magnitudes of steady torque and the measurement of the unit angle of twist with time using a specially developed multiaxial creep apparatus. Based upon the results, a nonlinear constitutive relation in shear involving two kernel functions has been obtained. Dilatational creep behavior was also studied by subjecting tissue samples to various magnitudes of hydrostatic stress and the measurement of the volume change with time. A rheological constitutive relation has been developed that agrees well with the dilatational creep test data. Finally, general rheological constitutive relations have been obtained by combining the constitutive relations for shear and dilatational deformations. In addition, creep behavior under uniaxial compressive loading has been predicted from the developed constitutive relations and compared with the experimental data. The predicted values have been found to agree with the experimental results.