Abstract The numerical solution of the inelastic response behaviour is explored on the constitutive level as well as on the structural level. In the first case explicit and implicit numerical schemes are examined for the solution of first order rate equations which are used to model the evolution of inelastic mechanisms. In the second case different inelastic analysis methods are studied after finite element projection of the local constitutive statements onto structural level. Aside from the traditional explicit initial load method, computational aspects are discussed for implicit solution schemes, some of which involve the evaluation and factorisation of tangent gradient matrices. A particularly useful technique is developed in the form of an iterative pseudo load method in which the stiffness matrix remains unchanged and where the local constitutive gradients are converted into equivalent initial loads. In this way the implicit algorithms require little additional computational effort to improve the accuracy and stability of the explicit formulations which are normally used for the incremental initial solution of creep problems.