As the experience from building practice shows, condensation in insulating materials can result in serious reduction of thermal properties and, in consequence, systemic upset of living qualities in dwellings. Moisture in building insulants can also affect an increased dust contamination, algae or mold growth as well as damages due to the frost formation occuring in winter periods. An understanding about this is good for knowledge of processes when high thicknesses of thermal insulation are used in cold climates and moisture might become trapped in the building envelope. Our research reports on a laboratory experiment of frost formation and moisture condensation in fibrous insulation based on stone wool. Frost formation in samples of stone wool open to air was noted in cases when the temperature field over the specimen was between + 20 and – 20ºC and the air on the warm side was saturated with moisture. Frost accumulated with time in the part of the specimen facing the cold air. In the part of the specimen facing the warm humid air condense formation occurred. In this part the material had moisture content considerably higher than what could be anticipated from data such as moisture isotherms.