Spudcan foundations are often pushed into a spatially varying non-homogeneous seabed to provide bearing capacity for a mobile jack-up platform. The natural variability of soil properties coupled with the complexity of loading conditions make determining the bearing capacity of spudcan foundations a challenging problem. A random finite element method is established to investigate the bearing capacity of a spudcan foundation embedded in a spatially varying clayey seabed when subjected to vertical, horizontal and moment loadings. A criterion is proposed for determining the characteristic value of the shear strength for the random seabed. Results indicate that the spatial variability in the clayey seabed significantly reduces the bearing capacity of a spudcan foundation. This reduction is more significant in the vertical bearing capacity than in the horizontal and moment bearing capacities. The mean bearing capacity is smaller for the clay with larger coefficient of variation of undrained shear strength. A characteristic value of mean minus a standard deviation of the undrained shear strength is capable to ensure the probability of failure is not greater than 5%. This study provide an evaluation method for the spatial variability effect of a clayey seabed, paving the way for a cost-effective design of spudcan foundations.