In dendrochemical studies, an analysis of wooden cores extracted from tree stems is a widely spread research method. A methodological problem is related to the method: whether a single core per tree can be representative of all the stems. The study aimed to estimate how the elemental contents are variable in the tree rings and whether the contents correlate among different cores. The cores were extracted from stems of Pinus sylvestris L., four cores per tree, according to the cardinal directions (east, west, north, south). The elemental contents (Al, Si, P, S, Cl, K, Ca, Ti, Mn, Fe, Cu, Zn, and Sr) were estimated through the X-ray fluorescent analysis facility Itrax Multiscanner (COX Analytical Systems). The agreement between the temporal series of different cores was estimated through Spearman’s correlation coefficients. It has been found that the temporal intra-tree series for almost all the studied elements do not correlate with each other. The exclusions are Ca and K which show strong consistent correlations. The source for the correlations is, however, the long-term trends from the pith to the bark. The detrending of the Ca and K series reveals some high-frequency correlations which are not consistent among the trees. At least for Scots pine, a single core is unlikely to be a reliable representative of the whole stem in the respect of elemental content. A few research directions to overcome the uncertainty has been discussed.