This paper describes a probabilistic study of the two dimensional bearing capacity of a vertically loaded strip footing on spatially random, cohesive soil using Random Field Numerical Limit Analyses. The analyses use a Cholesky Decomposition technique to represent the spatial variation in undrained shear strength within finite element meshes for both upper and lower bound analyses, assuming an isotropic correlation length. Monte Carlo simulations are then used to interpret the bearing capacity for selected ranges of the coefficient of variation in undrained shear strength and the ratio of correlation length to footing width.