Boundary element method (BEM) formulations for usual and sensitivity problems in small strain elastoplasticity, using the concept of the consistent tangent operator (CTO), have been recently proposed by Bonnet and Mukherjee. ‘Usual' problems here refer to analysis of nonlinear problems in structural and solid continua, for which Simo and Taylor first proposed the use of the CTO within the context of the finite element method (FEM). It was shown by Bonnet and Mukherjee that the sensitivity of the strain increment, associated with an infinitesimal variation of some design parameter, solves a linear problem which is governed by the (converged value of the) same global CTO as the one that appears in the usual problem. This paper presents a general numerical implementation of the above formulations. Numerical results for the usual and sensitivity problems are presented for a two-dimensional (plane strain) example. Sensitivities are calculated with respect to a material parameter that characterizes isotropic strain hardening. The crucial role of the CTO, in providing accurate numerical results for the mechanical variables as well as their sensitivities, is examined in this paper.