In this paper, an error on the constitutive law (labeled the dissipation error) is used to measure the quality of finite element computations of plastic and viscoplastic structures whose behavior is described by internal variables. This measure takes into account all the classical sources of error involved in the computation: the space discretization (the mesh), the time discretization and the iterative technique used to solve the nonlinear discrete problem. More specifically, to quantify the quality of the space and time discretizations, two quantities, called indicators, are introduced. The efficiency of both the error and the indicators is shown for several examples.