The aim of this thesis was to investigate the difference between containerboard materials strength and stiffness properties in tension and compression, how the mechanisms behind compressive and tensile properties are affected by the relative humidity of the ambient air and how the relative humidity affects the compressive response of the fibre network. These properties are used to predict the lifetime performance of corrugated boxes and to prevent early collapses of the boxes and thereby waste or harm of the transported goods inside. The work also discusses the methods used to evaluate the different properties and how reliable the results are. The experimental part includes testing of linerboard and fluting materials from both virgin and recycled fibres, which have been conditioned at 50% and 90% relative humidity. The compression tests were filmed to evaluate if different compression failure modes can be related to the strength and stiffness of the material. The results indicated that the compressive strength and stiffness differ from the strength and stiffness values in tension at 90% relative humidity. Compressive strength is lower in both 50% and 90% relative humidity compared with the tensile strength. However, the compression stiffness shows a higher value than the tensile stiffness at 90% relative humidity. The study of the method for evaluating the compressive behaviour of the paper does not present a complete picture on what type of failure the paper actually experience.