Simple analytical solutions exist for the deflection by line loads of thin elastic beams that overlie an inviscid fluid substrate. Deflections for more complex rectangular- and triangular-shaped loads can be evaluated by integration. The deflection of a beam that varies in thickness along its length is best solved, however, by numerical rather than analytical methods. Foremost among them are finite difference techniques, and both two- and three-dimensional codes are now widely available. Thin-plate theory and a flat Earth are good approximations to make in most geological modelling applications.

Modelling of stresses that influence glacially triggered faulting has progressed substantially in the last decades with more complex models and improved modelling techniques, incorporation of a variety of relevant processes, better constraints of ice-loading history, higher model resolution and 3D geometries. Some recent developments are collected in this section to portray the scope and variability of numerical modelling relevant to glacially triggered faulting. These range from modelling of the general in situ stress field to studies on the stress field induced by glacial loading and unloading.

An appropriate estimation of the ambient background stress field is crucial for determining the effect of additional ice loading (or unloading) on pre-stressed faults. Contributions from local and far-field stress sources (topography, tectonics) need to be reconciled with in situ measurements from boreholes and fault-plane solutions from earthquakes. We describe the different types of stresses in glaciated regions with a focus on Scandinavia together with the techniques used to incorporate stresses into numerical models.