AbstractEfficient solution of boundary value problems for time‐dependent inelastic deformation in metallic structures is of great practical importance. These problems are generally solved by finite element methods and separate descriptions for time‐independent plasticity and time‐dependent creep are normally used. The boundary–integral equation method was recently applied for the first time to such problems. This paper presents a very efficient numerical implementation of the method with a linear description of the relevant variables over each boundary element and a newly developed Euler‐type time‐integration scheme with automatic time‐step control for time integration. Numerical results for plates in plane stress with and without cutouts, under different loading histories, are presented. A combined creep–plasticity constitutive theory with state variables is used to model material behaviour. The results are more accurate and are obtained with much less computational effort compared to a previous attempt with an uniform description of variables over each boundary element and a predictor–corrector scheme for time integration. The computer program developed is quite general and can handle plane stress problems for plates of arbitrary shapes subjected to arbitrary time‐histories of loadings. The numerical results presented in the paper are for certain il