The cylindrical samples of ‘Beni Shogun’ apples cultivar in a range of deformation velocities from 0.0002 to 1 m s−1 were studied using stress relaxation tests. In the work, experimental courses of the force response were described via the Maxwell model, and the effects of deformation velocity on the Maxwell model parameters as well as the maximum and residual force were determined. The maximum force increased with the increase of the deformation velocity, which proved the response of apple flesh to be of viscoelastic nature. The residual force described the state of the material after the strain and was much higher under the quasi-static than impact loading conditions. The three relaxation times decreased with the increasing deformation velocity. For the shortest relaxation time (order of magnitude 0.1 s) there was a rapid decrease in the velocities under the quasi-static loading conditions and it remained on a steady and low level under the impact loading conditions. A definite limit was observed between the medium relaxation time (order of magnitude 1 s) for the lowest deformation velocity of 0.0002 m s−1 and the other relaxation times obtained at higher deformation velocities. The values of the longest relaxation time (order of magnitude 100 s) were much larger under the quasi-static than the impact loading conditions.