This study was aimed at evaluating the distribution of nutrients in the organs of silver birch growing on extremely nutrient-poor stands associated with inland dunes in central Poland. The study covered three stands, aged 12, 20, and 34 years. Ten average trees were sampled from each stand, including their fine roots, coarse roots, stemwood, bark, coarse branches, fine branches, and leaves. Under each tree, the soils were sampled at depths of 0–10, 10–20, 20–40, and 40–80 cm. The contents of nitrogen (N), phosphorous (P), potassium (K), calcium (Ca), magnesium (Mg), sulfur (S), iron (Fe), manganese (Mn), copper (Cu), and zinc (Zn) were analyzed in the biomass and soil samples. The studied soils were classified as Arenosols; they were strongly acidic and very poor in the studied elements. The nutrient distribution in the birch biomass was highly variable. Most had their highest concentrations in the leaves, followed by the bark (N, S, Cu), roots (P, K, Mg), and branches (Ca). The highest amounts of Fe were in fine roots, whereas Mn and Zn were most abundant in the bark. Wide variability was also apparent in the bioaccumulation factors. These were usually the highest in the leaves or bark and the lowest in the stemwood. Nitrogen showed the highest bioaccumulation intensity among the studied elements, followed by S, Zn, Cu, Mn, and P. The bioaccumulation intensity of the nutrients varied among the stands, in many cases showing significant correlations (both positive and negative) with stand age.