This thesis describes a numerical investigation of shallow circular foundations resting on various types of soil, mainly siliceous and calcareous sands. An elasto-plastic constitutive model, namely the MIT-S1 model (Pestana, 1994), which can predict the rate independent behaviour of different types of soils ranging through uncemented sands, silts and clays, is used to simulating the compression, drained triaxial shear and shallow circular foundation responses. It is found that this model provides a reasonable fit to measured behaviour, particularly for highly compressible calcareous sands, because of the superior modelling of the volumetric compression. The features of the MIT-S1 model have been used to investigate the effects of density, stress level (or foundation size), inherent anisotropy and material type on the response of shallow foundations. It was found that the MIT-S1 model is able to distinguish responses on dilatant siliceous and compressible calcareous sands by relatively minor adjustment of the model parameters. Kinematic mechanisms extracted from finite element calculations show different deformation patterns typical for these sands, with a bulb of compressed material and punching shear for calcareous sand, and a classical rupture failure pattern accompanied by surface heave for siliceous sand. Moreover, it was observed that the classical failure pattern transforms gradually to a punching shear failure pattern as the foundation size increases. From this evidence, a dimensional transition between these failure mechanisms can be defined, referred to as the critical size. The critical size is also the limiting foundation size to apply conventional bearing capacity analyses. Alternative approaches are needed, focusing mainly on the soil compressibility, for shallow foundations greater than the critical size. Two approaches, 1-D compression and bearing modulus analyses, have been proposed for those foundation conditions. From the validations, the former is applicable for extremely large foundations, very loose soil conditions and highly compressible calcareous materials, while the latter is suitable for moderate levels of compressibility or foundation size. It is suggested that appropriate assessment of compression features is of great importance for shallow foundation analysis on sand.