The application of the cantilever bending technique to stress measurements at surfaces and in epitaxial films is elucidated. The role of elastic anisotropy in quantitative cantilever curvature analysis is discussed. The stress in Co monolayers is measured during epitaxial growth on Cu(001). The Co-induced stress is found to oscillate with a period of one atomic layer. Simultaneous stress and medium-energy electron diffraction identify maximum stress for filled Co layers. Strain relaxation in Co islands leads to the reduced stress contribution of 2.9 GPa in the partially filled top layer as compared to 3.4 GPa for the filled layers. The cantilever technique is also applied to measure magnetoelastic properties of nanometre thin epitaxial films. Our measurements reveal that the magnetoelastic-coupling coefficients in epitaxial Fe, Co and Ni films differ from the respective bulk values. It is proposed that the epitaxial misfit strain is of key importance for this peculiar magnetostrictive behaviour of ultrathin films.