This dissertation presents an investigation of the effects of stress, and of absolute and relative particle size, in tests on vertically loaded footings. Two granular materials, namely, a silica rock flour and a Chatelet flint grit, which differed in nominal diameter by a factor of 50 but were otherwise practically similar in all other grain characteristics were used in this work. A comprehensive series of triaxial tests under a wide range of cell pressures was carried out to quantify the stress and absolute particle size effects. Model footing tests were also performed by pushing a rigid circular punch axisymmetrically into the flat surface of a cylindrical soil model either under 1-g (gravity) with surcharge or under elevated g in a centrifuge. The 1-g and centrifuge test series were used to study the scale effects on the surcharge term Ng and the self-weight term Nγ of the Terzaghi bearing capacity equation, respectively. Parameters varied were punch diameter, particle size and surcharge or g level. Two theoretical analyses were attempted based on the finite element method and the method of characteristics. Using the Schofield Soil Model, the finite element analysis can give a reasonable order of magnitude prediction for the settlement of the footing under working load conditions. When the effect of reducing angle of shearing with increasing stress was taken into account together with the change of geometry due to footing penetration, the angles of shearing inferred from the method of characteristics fall within ±20 of those measured in triaxial compression tests. Distortion due to violating the scaling law by not conserving the ratio of particle size to model dimension was not considered to be significant. Distortion due to violating the constitutive soil behaviour by varying the absolute particle size was found to be significant due to differences in grain crushing, but this can be accounted for effectively by the new style of calculations developed in the thesis.