Professor Sloan has made fundamental contributions to the science of computational geomechanics. He has been the key architect of new numerical methods which enable engineers to predict the maximum load capacity of general types of geostructures (such as tunnels, dams, highways and foundations). These methods are based on the limit theorems of plasticity, finite elements, advanced optimisation algorithms and adaptive remeshing, and have been extended to model cyclic loading. Sloan has also derived important new algorithms for implementing complex soil models, solving nonlinear finite element equations, generating finite element grids, and solving large systems of sparse equations.