The prevalence of hypertension increases with age, but the mechanisms linking this phenomenon are not well understood. Hydrogen sulfide (H2S) may be involved in this process, as it plays a role in the cardiovascular system, affecting blood pressure and heart and kidney functions. The aim of this study was to evaluate the influence of hypertension and aging on sulfur-containing compounds metabolism in the hearts and kidneys of Wistar Kyoto (WKY) and Spontaneously Hypertensive Rats (SHR) of different age groups. We determined the expression and activity of four enzymes participating in H2S production: cystathionine beta-synthase (CBS), cystathionine gamma-lyase (CTH), 3-mercaptopyruvate sulfurtransferase (MPST), and thiosulfate sulfurtransferase (TST). The levels of reduced/oxidized glutathione, cysteine, cystine, and cystathionine, and the ability of tissues to form hydrogen sulfide were also investigated. Tissues obtained from younger WKY rats produced the highest amounts of H2S. The effect of hypertension on the metabolism of sulfur-containing compounds was manifested by a decrease in sulfane sulfur concentrations in heart homogenates and a decrease in CTH activity in the kidneys. The hearts and kidneys of older WKY rats were characterized by lower MPST or CTH gene expression, respectively, compared to younger animals. Our study demonstrates that hypertension and aging influence cardiac and renal sulfur-containing compounds metabolism and reduce H2S production. Furthermore, we showed that MPST plays a major role in the production of hydrogen sulfide in the heart and CTH in the kidneys of rats.