A dual‐screen computed radiography (CR) technique has been developed to improve and optimize the overall image signal‐to‐noise ratio (SNR) and contrast‐to‐noise ratio (CNR). With this technique, two CR screens are exposed together and separately scanned to form a front and a back image. These two images are then superimposed to form an image of improved SNR and CNR. A mathematical model has been derived to describe the improvement and optimization of the SNR and CNR. Based on this model, the front and back images should be weighted in proportion to their SNR squared to optimize the SNR of the composite image. Imaging experiments have been conducted to verify the theoretical model under mammographic and chest imaging conditions. The results largely agree with the theoretical predictions. It has also been found that optimization of the SNR results in nearly optimal CNR and vice versa. For mammographic imaging, a 14%–22% improvement in the SNR and a 13%–19% improvement in the CNR have been demonstrated. For chest imaging, a 31%–36% improvement in the SNR and a 28%–30% improvement in the CNR has been demonstrated.