In the theoretical study of vacuum-powered artificial muscles, the inhomogeneous and nonlinear deformation properties of the skin have not been fully investigated, and the effect of the skin material on their performance has not been considered in the model. This work presents a theoretical analysis for the support-skin vacuum-powered artificial muscles and extends the skin to more general flexible materials, which endows the results with a strong generalization ability. The influence of various factors including structural parameters, axial force, negative pressure, and material parameter on the skin deformation are comprehensively analyzed, which is directly related to the actuation behaviors. Besides, the theoretical analysis is able to make an accurate prediction of the wrinkling behavior of the skin, including the critical boundary and wrinkling region. The experimental verification on the theoretical predicted configuration and wrinkled area of the skin have been carried out, which verifies the correctness of the results of the theoretical analysis. We believe that this work will provide an effective way for guiding the design and analyzing the actuation properties of such artificial muscles.