<p>The compactness and high heat transfer efficiency of Printed Circuit Heat Exchangers (PCHEs) benefit from their dense microchannel networks, but they also introduce multiscale complexities to global thermal stress analysis. In this paper, a homogenization method is proposed for predicting the global temperatures of the fluids and solid, as well as the corresponding thermal stress in PCHEs under steady-state conditions. PCHE cores are modeled as homogeneous media, and the volume-averaged temperatures and stress are adopted as macroscopic variables in the coupled governing equations, where all the equivalent parameters are determined by the Representative Volume Element (RVE) model. To validate the proposed homogenization method, a Homogenization Finite Element Model (HFEM) was developed for a counter-flow PCHE core with 150 channels, and was compared with the Classical Finite Element Model (CFEM). Although the macroscopic temperatures predicted by HFEM for both cold and hot fluids cannot reflect microscale temperature variations in channel flows, they generally matched the cross-sectional average temperatures of the flows obtained from CFEM. Because the solid temperature variation between adjacent cold and hot channels was much smaller than the global variation, the macroscopic solid temperature from HFEM was comparable to the microscale solid temperature from CFEM. Both models consistently predicted that the hot fluid inlet region sustained elevated thermal stress, and the membrane and bending stresses in the channel ridges decreased gradually from the hot channel inlet to the cold channel inlet. Despite minor discrepancies between CFEM and HFEM, HFEM reduced the CPU time for temperature and mechanical calculations by factors of 40 to 75 and 10 to 15, respectively.</p>