An algorithm is outlined for the implicit integration of isotropic plasticity models for an arbitrary choice of mixed stress and strain control variables. Drained as well as undrained behaviour is considered. The closest-point-projection method in conjunction with a completely strain-driven format is used in a core algorithm. In the drained case strain response variables are determined via iterations to satisfy equilibrium of prescribed and calculated stresses that correspond to the strain response variables. In the undrained case, on the other hand, strains and pore pressure are determined via simultaneous iterations to satisfy equilibrium and the incompressibility condition. The algorithm is applied to a new generalized cam-clay model, and various iteration techniques are assessed. In particular, Newton iterations which employ the matrix of algorithmic tangent stiffness moduli are shown to compete favourably with more conventional methods.