In the present contribution, we design a modelling and numerical scheme to study the occurrence of elasto-plastic behaviour in layered systems. In this sense, we circumscribe our attention to deformable one-dimensional bodies interacting with a rigid substrate by means of a layer of adhesive-like material. Within this simplified setting, we are able to simulate and describe the behaviour of the physical quantities of interest and to have an insight, at least numerical, concerning the length of the zone in which exchanges of forces are present. The latter, being non-uniform along the system under study, induces a non-uniform development of plastic distortions, in agreement with a generalised shear lag effect. We remark that the present work is part of an ongoing research, whose results are collected in a manuscript to be sent to a scientific journal.