A novel testing methodology for the characterization of viscoplastic (VP) deformation of unidirectional (UD) composites under transverse tensile loading is described. The law of transverse VP deformation, which, due to specimen failure, is almost impossible to obtain using UD specimens, is identified from curvature changes of an unsymmetrical CF/EP [0/90] specimen. An initially thermally curved specimen is loaded in the axial direction to different high levels of tensile strain, with a specified holding time. After unloading and waiting for recovery of the viscoelastic strains, the curvature of the specimen had changed due to the irreversible transverse VP strain and microdamage had developed in the 90° ply. The damage effect is incorporated into the model by introducing the“effective stiffness” of the damaged layer, which is a function of the crack density and the local delamination length. A model based on the classical laminate theory is used to construct a relationship between the measured curvature after a loading step and the accumulated VP strain, temperature, and the effective stiffness. The back-calculated VP strains are analyzed, and their functional dependence on the stress and time in the viscoplasticity law is obtained. The model and the methodology are validated by comparing calculation results with test data for [902/0] laminates subjected to a similar loading. The methodology suggested could be very accurate on using a laminate with ultrathin plies in the test. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.