The problem of estimating bounds to shakedown loads for problems governed by a class of deviatoric plasticity models including those of Hill, von Mises, and Tresca is addressed. Assuming that an exact elastic solution is available, an upper bound to the elastic shakedown multiplier can be obtained relatively easily using the plastic shakedown theorem. A procedure for computing this upper bound for arbitrary load domains is presented. A number of problems are then examined and it is found that the elastic shakedown factor is given as the minimum of the plastic shakedown factor and the classical limit load factor. Finally, some exact solutions to a number of two dimensional problems are given.