As a part of ARIES-ACT research, we have been performing a detailed re-examination of requirements and design of vacuum vessels for fusion power plants. This paper discusses structural analysis performed in support of this examination. We have performed parametric 3-dimensional finite element analyses of ARIES-ACT-type vacuum vessels. The vacuum vessel structure is subjected to different types of loads such as atmospheric pressure, weight of the vessel itself and off-normal loads such as over-pressurization due to a leak in fusion core components, electromagnetic forces from disruptions, etc. Ribbed structure is considered in order to minimize the thickness of the vacuum vessel as well as to cool the system. We will discuss our results including structural response to various loads and trade-offs among structural design choices.