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For product packaging, the visual elements in it can further enhance the appeal of the package to customers. This article briefly introduces visual elements and packaging design and made an example analysis with the gift packaging design of Squirrel Design Studio. In the case study, the packaging design of the studio’s mirror, storage bag, and puzzle was rated by hierarchical analysis and questionnaires, and the packaging design was analyzed based on the rating results. A convolutional neural network (CNN) was also used to evaluate packages in batches. The results showed that the CNN could make a batch evaluation of gift packaging design accurately; the three gift packaging designs were based on the studio’s logo, making the ratings similar; in addition, the packaging design patterns were composed of different geometric shapes to show the studio’s innovative design theme, and the squirrel silhouette and text description were used to strengthen the impression of the studio among customers.