The results of this study provided accurate guidance on the possibility of using common buckwheat (Fagopyrum esculentum Moench) in phytoremediation practices for mineral soil or organic soils contaminated with Cd or Pb. Based on a model pot experiment, the tolerance of buckwheat to elevated contents of cadmium and lead in organic and mineral soils was examined. The soils were differentiated into neutral and acidic, and amended with metals at doses of 10 mg Cd kg−1 DM and 100 mg Pb kg−1 DM of soil. The growth, development, biomass, translocation coefficient, and tolerance index (TI) of the tested plants were examined. The use of metals caused a weakening of plant growth and development, as well as intensified chlorotic and necrotic changes to the buckwheat leaves. The application of Cd caused a statistically significant decrease in shoot biomass. The plants growing in organic acidic soil were most vulnerable to Cd toxicity. The (TI) values confirm the generally low tolerance of buckwheat to Cd, except for the treatment in organic neutral soil, and the high tolerance of this plant to Pb in all the studied soils.