It is important to develop research on sealing materials in order to find effective solutions to ensure the energy efficiency of buildings. The aim of this study is to investigate the peel adhesion of single-sided self-adhesive tapes to different construction surfaces and to determine the change in this characteristic due to climatic effects. Different construction tapes, mostly used externally in buildings, are glued to different substrates. The artificial aging of test samples was carried out, simulating the effects of moisture, heat, and cold; the intensity, duration, and sequence of the cyclic effects were determined, taking into account the statistical climatological data of the middle-latitude climate zone. The peel adhesion of the tapes was determined before and after different numbers of artificial aging cycles. The results show that the peel adhesion range is very wide, from 11 to 61 N/24 mm. In most cases, a lower-rated peeling adhesion was obtained by peeling the tape from plastered cement–sawdust board. The change in peel adhesion depends more on the surface to which the tape is glued than it does on the number of climatic exposure cycles selected for the test.