A simplified three‐dimensional viscoelastic equation, based on the Green–Rivlin theory, was used to characterize the nonlinear creep behavior of two food products, i.e., apple and potato. Uniaxial and triaxial creep tests were conducted to evaluate the nonlinear behavior of apple and potato flesh. Four material property functions in the nonlinear constitutive equation were determined using experimental results. The nonlinear constitutive equation was then used to predict the load response of both apple and potato flesh under various loading conditions. The nonlinear constitutive model calculated values compared favorably with the experimental data. Results show that the nonlinearity of apple flesh under the uniaxial creep loading was significant especially for extended loading time periods. The initial load response has a pronounced effect on the nonlinearity of potato flesh under the uniaxial creep loading.