Laboratory tests on London Clay (Hight et al., 2007) have highlighted two key observations: softening on fissures in triaxial extension tests, and softer torsional shear behaviour in the hollow cylinder apparatus (HCA). Existing constitutive models have been unable to replicate these observations in a way which reflects fissure softening in London Clay. This paper presents two constitutive models which incorporate fissure softening. Softening occurred only on sub-horizontal and sub-vertical fissure planes, and initiated if the friction angle on one of these planes exceeded a critical value. One model reduced stiffness components isotropically, whilst the other softened only shear stiffness along the fissure plane. Both models were evaluated by simulating laboratory tests. The model softening on the fissure plane failed to simulate softening in extension, and generated unrealistic stress paths in the HCA. This suggested that the mechanism of fissure softening is more complex than a simple slip plane. However, the model which softened isotropically replicated both observations successfully, demonstrating its potential to improve the simulation of London Clay behaviour in large-scale numerical analyses.