This paper presents the results of quasi-static tests carried out using a texturometer and of impact tests combined with stress relaxation on a stand equipped with a heavy pendulum of the hammer type. The tests were carried out using fresh roots and those stored at 20 °C for 120 h. The impact velocities Vd were 0.001, 0.002, 0.01, 0.02, 0.75, and 1.25 m·s−1. Compiling the relaxation times T1 for Vd indicated their large drops for both fresh and stored roots. The largest average values T1 were obtained in the range from 0.197 s to 0.111 s at the small velocities of deformation 0.001–0.02 m·s−1 and the smallest ones in the range from 0.0252 to 0.0228 s at the Vd equal to 0.75 and 1.25 m·s−1. A decrease in T2 values was observed in the average range of 8.02–4.27 s at Vd = 0.001–0.02 m·s−1 for fresh beets. For the velocities 0.75 m·s−1 and 1.25 m·s−1 and stored roots, the range of average values was smaller and ranged from 6.13 s to 4.54 s. The reaction forces of the Fp sample reached the highest average levels from 168.2 N to 190.8 N for fresh roots and 46.5 to 56.2 N for 5-day-old roots. However, the lowest Fp was recorded at speeds (0.001–0.02 ms−1) 57.5–62.3 N for the fresh roots and 46.5–56.2 N for the 5-day-old roots. For the velocities greater than 0.75 m·s−1 and 1.25 m·s−1, the values of reaction forces increased at the average values 168.2–190.8 N for the fresh roots and 158.2–175.4 N for 5-day-old ones.