A fully coupled moisture-displacement finite element model has been developed to predict the viscoelastic, mechano-sorptive and swelling/shrinkage behaviour of FRP reinforced timber elements when stressed under long-term load and simultaneously subjected to changes in relative humidity. A DFLUX subroutine, to describe the changes in relative humidity with time, and a UMAT subroutine, implemented to describe the viscoelastic, mechano-sorptive and swelling/shrinkage behaviour, are presented. Additionally, an irrecoverable mechano-sorptive component is presented. This additional irrecoverable component occurs when the timber moisture content increases to a moisture content above levels previously attained. The model is found to be in agreement with experimentally determined deflection and strain results on both unreinforced and FRP reinforced beams subjected to constant and variable climates. (C) 2020 Elsevier Ltd. All rights reserved.