Anhydrite and gypsum minerals in claystones are found in different configurations: isolated nodules, filled veins, continuous layers, massive bodies and combinations of these geometrical structures. Continuous or, better, quasi-continuous records of anhydrite and gypsum content measured in boreholes show frequently a marked spatial variability. This heterogeneity may explain to some extent the variability observed in surface heave measurements and swelling pressures measured against structures such as tunnel linings. An additional cause of observed heave and pressure concerns the presence of discontinuities and open pore space required for the precipitation of gypsum crystals. In all cases water should be present. The paper describes two cases that illustrate the relevance of spatial variability of swelling strains and its identification.The first case analyses the origin of the surface heave recorded in a large power station founded on an Eocene anhydritic marl, fairly homogeneous at a large scale. The marl heave was triggered by two modifications of the initial state of the marl: i) a large excavation and its induced vertical tensile strains capable of opening fissures along stratification planes and ii) the establishment of a table water level that wetted the marl through the open discontinuities. The paper describes long term records of heave strains measured by high precision extensometers, the model developed to quantify the surface heave and its comparison with long term records. In a second case, a highly instrumented concrete rigid circular tunnel lining provided data on recorded swelling pressures at the claystone-invert interface and on the measured strains in reinforcing steel bars. This information was processed to derive the histogram of observed stationary boundary swelling pressures. In addition, the strains records measured on the lining reinforcement provided a benchmark for the 3D model built to relate swelling pressures and internal lining stresses. The procedure led to an approximation of the distribution and intensity of swelling forces against the tunnel lining. This analysis, based on long term real data, helped to define new design criteria, more accurate and substantially cheaper, for tunnels excavated in the same geological formation. The paper concludes by suggesting a set of recommendations to limit the risk of damaging swelling of anhydritic rocks and some comforting actions which may be adopted when the swelling phenomenon has initiated.