Biomass allometric relations are necessary for precise estimations of biomass forest stocks, as well as for the quantification of carbon sequestered by forest cover. Therefore, we attempted to create allometric models of total biomass in young silver birch (Betula pendula Roth) trees and their main components, i.e., leaves, branches, stem under bark, bark, and roots. The models were based on data from 180 sample trees with ages up to 15 years originating from natural regeneration at eight sites in the Western Carpathians (Slovakia). Sample trees represented individuals with stem base diameters (diameter D0) from about 4.0 to 113.0 mm and tree heights between 0.4 to 10.7 m. Each tree component was dried to constant mass and weighed. Moreover, subsamples of leaves (15 pieces of each tree) were scanned, dried, and weighed. Thus, we also obtained data for deriving a model expressing total leaf area at the tree level. The allometric models were in the form of regression relations using diameter D0 or tree height as predictors. The models, for instance, showed that while the total tree biomass of birches with a D0 of 50 mm (and a tree height of 4.06 m) was about 1653 g, the total tree biomass of those with a D0 of 100 mm (tree height 6.79 m) reached as much as 8501 g. Modeled total leaf areas for the trees with the above-mentioned dimensions were 2.37 m2 and 8.54 m2, respectively. The results prove that diameter D0 was a better predictor than tree height for both models of tree component biomass and total leaf area. Furthermore, we found that the contribution of individual tree components to total biomass changed with tree size. Specifically, while shares of leaves and roots decreased, those of all other components, especially stems with bark, increased. The derived allometric relations may be implemented for the calculation of biomass stock in birch-dominant or birch-admixed stands in the Western Carpathians or in other European regions, especially where no species- and region-specific models are available.