Based on hydrodynamics and elastic mechanics, a model is proposed for the aspheric encapsulated bubble (AEB) in liquid driven by a spherical ultrasound. The aspheric component of the bubble surfaces includes any complicated shape as a perturbation of the spherical symmetry. For example, the simple ovoid encapsulated bubble is studied numerically in the framework of this model. The results show that (1) the AEB will keep a stable aspheric oscillation under the spherical acoustic drive, which is impossible for the cavitation bubble; and (2) apart from the initial aspheric shape, the thickness distribution of the shell is an important factor to the AEB's oscillation. Apparently, the thinner shell is less stiff so that it has a relatively larger pulsation amplitude. Thereafter the dependence of the AEB's pressure resistance against rupture on its asphericity is presented. The asphericity is shown to degrade the encapsulated bubble's bearable driving pressure.