As boilers are designed with higher parameters and larger capacity, deformation failure caused by thermal stress seriously threatens the safety of heating surfaces, especially membrane walls. In this paper, thermal strain/stress distribution on membrane walls, and its relationship with heat transfer process in the furnace were experimentally investigated in a laboratory-scaled arch-fired boiler. Tension strain and compression stress were detected on membrane walls, with definite directionality decided by wall structure. The measured high stress and high temperature zones coincided well with the location of deformation failure in the prototype boiler. Temperature on membrane walls links the heat transfer process and strain/stress distribution. A high level of wall temperature enhanced the directionality of strain/stress, while dispersive temperature gradient weakened such directionality. Additionally, significant correlations were found between wall temperature and corresponding thermal strain/stress. By defining constraint coefficients (beta(1), beta(2)) and stress coefficients (k(e), k(tau)), a model was proposed to quantitatively predict the strain/stress distribution on membrane walls. It provides a way to reduce the deformation risk of membrane walls via improving heat transfer process. Furtherly, the temperature-strain/stress correlations found in the arch-fired boiler were validated in another wall-fired boiler, thus provide great value in safety precaution to various boiler types. (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.