Understanding the thermomechanics of flexible, axially moving webs subject to heat flux is important for ensuring process stability and product quality in roll-to-roll (R2R) flexible electronics manufacturing and nano-manufacturing. These applications include processes such as drying, curing, heat annealing, laser processing, plasma processing, functional printing, etc. A mathematical model for predicting the temperature and stress distributions in an axially moving web under arbitrary shape of heat flux is presented, including axial transport, heat conduction, convective heat transfer, and thermal radiation. A MATLAB based nonlinear finite element code is developed to predict the temperature and stress fields during such processes. The experimentally measured temperature distribution in moving paper and PET webs subject to heating from an IR laser source is compared with theoretical predictions to validate the computational approach. Such computational models are expected to aid in the development of a range of R2R processes where temperature gradients and stress fields can influence the product quality or lead to mechanical instabilities such as wrinkling or excessive web vibration. (C) 2018 Elsevier Ltd. All rights reserved.