An available novel system for studying the cellular mechanobiology applies an equiaxial strain field to cells cultured on a PolyDiMethylSiloxane (PDMS) substrate membrane, which is stretched over the deformation of a cylindrical shell. In its application of in vitro cell culture, the in-plane strain of the substrate membrane provides mechanical stimulation to cells, and out-of-plane displacement plays an important role in monitoring the cells by a microscope. However, no analysis of the parameters has been reported yet. Therefore, in this paper, we employ analytical and computational models to investigate the mechanical behavior of the device, in terms of in-plane strain and out-of-plane displacement of the substrate membrane. As a result, mathematical descriptions are given, which are not only for quantitatively determining the applied load, but also provide the theoretical basis for the researchers to carry out structural modification, according to their needs in specific cell culture experiments. Furthermore, by computational study, the elastic modulus of PDMS is determined to allow the mechanical behavior analysis of a fabricated device. Finally, compared to the experimental results of characterizing a fabricated device, good agreement is obtained between the predicted and experimental results.