The cause of the stability of cratons, the old cores of continents, is still an enigma. Seismic studies have found that velocities within the cratonic lithosphere are quite variable laterally and in depth. Understanding the nature of this variability may provide information on how cratons are formed and stabilised. In this thesis, I perform a search of plausible thermal and compositional structures of cratonic lithosphere based on heat flow and xenolith constraints to model (using thermodynamic methods), seismic velocities and surface-wave dispersion curves for five different cratons. Sensitivity analyses show that the reasonable assumption of steady-state conductive temperature structure does not allow for sufficient variations in the thermal gradient to match seismic observations and varying the degree of depletion of compositions in the dunite-peridotite range only effects small changes in seismic velocity. We show that for the Kaapvaal, Yilgarn, Slave and Finland cratons, introducing metasomatic minerals (with up to 1 wt% water or 5 wt% carbonate) in the upper parts of the mantle lithosphere, significantly improves the fit to surface wave dispersion curves. The amount of metasomatic material required correlates with increased evidence for magmatic activity in the form of kimberlites. To match 3D seismic heterogeneity in the Eastern Canadian Shield, we require significant lateral variations in the amount of metasomatic minerals, with less modification of Archean Superior than Proterozoic Grenville lithosphere. Larger amounts of metasomatic minerals appear to correlate with geological evidence for magmatic activity, either arc-related during formation, or hotspot related at a later date. Significant concentrations of metasomatic minerals have been previously proposed to explain enigmatic mid-lithospheric discontinuities in old lithosphere. In addition, such modification, if pervasive enough to affect surface wave dispersion observations, could contribute to stable density stratification of the cratonic lithosphere.