The development and implementation of a complex numerical model for the determination of the damage to masonry buildings resulting from tunnelling settlements is described in this thesis. The current methods of damage prediction do not, in general, take into account the stiffness and weight of the surface structure. The model addresses this deficiency by explicit inclusion of the structure. Three-dimensional finite elements are used to model the ground with a non-linear, elasto-plastic soil model based on kinematic hardening. Tunnel linings are modelled using a novel overlapping elastic shell element: volume loss being simulated by shrinkage of linings coincidentally with excavation. Structures are modelled as collections of facades comprised of plane stress elements using a non-linear material model for masonry, similar to elastic-no tension. In developing the three-dimensional model, its two-dimensional counterpart is also studied. While the beam and shell elements used for linings (in two- and three-dimensions respectively) have the advantage of no rotational degrees of freedom the need to model boundary conditions at the element stiffness level complicates implementation. Tests using the shell elements show them to be satisfactory for the purpose of modelling tunnel linings. Results from a small number of analyses are given for construction of a straight tunnel beneath simple masonry structures. It is shown that the effect of the building on settlements depends heavily on its location in plan with respect to the tunnel axis. Predictions of crack patterns using the model for these analyses show that facades which the tunnel passes under first are less damaged than those later in the excavation sequence. Both of these conclusions serve to demonstrate that the problem can only be realistically modelled using three-dimensional methods. At present, however, the computer resources required to run the three-dimensional model are considerable.