The accuracy of integration of the constitutive equations for an isotropic elastic-perfectly plastic von Mises material is examined. A strainrate vector of arbitrary direction, but constant in time, is imposed for an arbitrary duration on a material with an arbitrary initial stress state. An exact solution is presented and then used to compare the accuracy of three commonly used numerical methods. The simplistic radial return method is found to have reasonable single step accuracy. It is recommended for moderate accuracy requirements and the exact method for higher accuracy. The multistep error estimator based on the magnitude of the deviatoric trial stress is shown to be bad and a better estimator presented for the secant stiffness method.