The model uncertainties for the static analysis (determination of the settlement at a given load and the ultimate bearing capacity) of square foundations on sand under axial compression are characterized using 67 field load tests. The model uncertainty for calculating the ultimate bearing capacity is represented by a ratio (model factor) of measured capacity to calculated capacity. The capacity model factor is found to be significantly affected by the foundation width. This statistical dependency is expressed as an exponential function. The residual part of the model factor is characterized as a lognormal random variable. A hyperbolic equation with two curve-fitting parameters is used to estimate the load-settlement curves normalized by measured capacity. Using the same database, the best-fit copula for the hyperbolic parameters is Gaussian copula.