Mat footings are used when the building load is so high, that spread or strip footings could not bear the weight or their employment would be inefficient. Furthermore, mat footings are helping to reduce the varying settlements caused by construction on non-homogenous soils or uneven load distribution on the footing.
The program GEO5 Slab can be used for the design of mat foundations or slabs of any shape on elastic subsoil, using the Finite Element Method.
Further sources:
Online Help - Program Slab