This paper concentrates on the fact that natural materials are variable, and that representation of this variability appears crucial to getting a realistic understanding of certain geotechnical problems. In this case, finite elements have been used to assess the influence of heterogeneity on the stability of a clay slope, characterized by a spatially varying undrained shear strength cu. For low to intermediate values of the coefficient of variation (e.g. 0.1–0.3), as are often observed in practice, pointwize variability can be approximated by a normal distribution. Data on spatial variability are more scarce, although vertical scales of fluctuation are usually much smaller than horizontal scales of fluctuation, and will often be small relative to the height of a slope. The results show that, for a given factor of safety, reliability is greatest for cu constant with depth. For cu increasing linearly with depth, reliability decreases due to the greater range of possible rupture surfaces: hence, in conventional (deterministic) design, higher factors of safety (or lower characteristic values) would be needed. In this study, horizontal anisotropy (of the heterogeneity) causes modest changes in reliability. However, problems are identified in which anisotropy is likely to have a significant influence.