This paper presents an analysis of Nemat-Nasser's (1991) explicit algorithm and a radial return algorithm for isotropic Von Mises materials undergoing large deformations. It is found that the final-radial return algorithm can result in a simple scalar equation (for the constant of proportionality that defines the plastic flow), which can be easily solved. A new modified algorithm is also proposed. All the three algorithms are efficient. No iterative scheme is required. For proportional loading, all the three algorithms work well. But, in cases where the direction of stress cannot well follow the direction of the deformation rate, which occurs when spin effect is significant or when the direction of deformation rate keeps changing, the explicit algorithm has a problem with its convergence; the final-radial return algorithm oscillates for large time steps; while the presently proposed modified algorithm can provide reasonable results even for large time steps, without any convergence problems.