•We study the mutual orbit period change of asteroid Didymos by the DART impact.•Shape deformation causes additional change in the mutual orbit period of Didymos.•Further analyses of this scenario allow for better evaluating the DART impact. The Asteroid Impact & Deflection Assessment (AIDA) targets binary near-Earth asteroid (65803) Didymos. As part of this mission, the NASA-led Double Asteroid Redirection Test (DART) will make a kinetic impactor collide with the smaller secondary of Didymos to test kinetic impact asteroid deflection technology, while the ESA-led Hera mission will evaluate the efficiency of the deflection by conducting detailed on-site observations. Research has shown that the larger primary of Didymos is spinning close to its critical spin, and the DART-impact-driven ejecta would give kinetic energy to the primary. It has been hypothesized that such an energy input might cause structural deformation of the primary, affecting the mutual orbit period, a critical parameter for assessing the kinetic impact deflection by the DART impactor. A key issue in the previous work was that the secondary was assumed to be spherical, which may not be realistic. Here, we use a second-order inertia-integral mutual dynamics model to analyze the effects of the shapes of the primary and the secondary on the mutual orbit period change of the system. We first compare the second-order model with three mutual dynamics models, including a high-order inertia-integral model that takes into account the detailed shapes of Didymos. The comparison tests show that the second-order model may have an error of ∼10% for computing the mutual orbit period change, compared to the high-order model. We next use the second-order model to analyze how the original shape and shape deformation change the mutual orbit period. The results show that when the secondary is elongated, the mutual orbit period becomes short. Also, shape deformation of the secondary further changes the mutual orbit period. A better understanding of this mechanism allows for detailed assessment of DART’s kinetic impact deflection capability for Didymos.