In this study, the model proposed by Yang et al. to generalize the stress–strain model for unconfined concrete with consideration of the size effect is expanded. Sim et al.’s compressive strength model that is based on the function of specimen width and aspect ratio was used for the maximum stress. In addition, a strain at the maximum stress was formulated as a function of compressive strength by considering the size effect using the regression analysis of datasets compiled from a wide variety of specimens. The descending branch after the peak stress was formulated with consideration of less dissipated area of fracture energy with the increase in specimen width and aspect ratio in the compression damage zone (CDZ) model. The key parameter for the slope of the descending branch was formulated as a function of specimen width and aspect ratio, concrete density, and compressive strength of concrete considering the size effect. Consequently, a rational stress–strain model for unconfined concrete was proposed. This model explains the trends of the peak stress and strain at the peak stress to decrease and the slope of the descending branch to increase, as the specimen width and aspect ratio increase. The proposed model agrees well with the test results, irrespective of the compressive strength of concrete, concrete type, specimen width and aspect ratio. In particular, the proposed model for the stress–strain curve rationally considered the effect of decreasing peak stress and increasing the descending branch slope, with the increase in specimen width and aspect ratio.