Vibration from equipment mounted on the telescope and in summit support buildings has been a source of performance degradation at existing observatories, for adaptive optics performance in particular. To ensure that that the total optical performance degradation due to vibration is less than the corresponding optical error budget allocation, a vibration budget has been created that specifies allowable force levels from each source of vibration in the observatory (e.g., pumps, chillers, cryocoolers, etc.). In addition to its primary purpose, the vibration budget allows us to make design trade-offs, specify isolation requirements for equipment, and tighten or widen individual equipment vibration specifications as necessary. Defining this budget relies on two types of information: (i) vibration transmission analysis that determines the optical consequences that result from forces applied at different locations in the Observatory and at different frequencies; and (ii) initial estimates for plausible source amplitudes in order to allocate force budgets to different sources in the most realistic and cost-effective manner. The transmission of vibration from sources through to their optical consequences uses the finite element model of the telescope structure, including primary mirror seg- ment models and control loops. Both the image jitter and higher-order deformations due to M1 segment motion are included, along with the spatial- and temporal-correctability by the adaptive optics system. Measurements to support estimates of plausible soil transmissibility are described in a companion paper. As the detailed design progresses and more information is available regarding what is achievable at realistic cost, the vibration budget will be refined.