The mechanical contribution to tissue behaviour is an important part of tissue development, homeostasis, and disease. Mechanical models of tissues are used in many areas of study including simulations, tissue engineering and the development of replacement parts for the body, and Optical Coherence Elastography where models are used for verification. Discovering some of the behaviors of tissue due to the structure alone will give more insight into the mechanics and behavior tissues. Structures that have tension as a main component of their architecture are called tensegrities and have different behaviors from normal structures that are mainly built to withstand compression. A model consisting of a single layer of three cells and their attachments was developed using simple tensegrities as a base structure. Tensegrities are formed of a truss structure of strings and bars where the tensioned strings hold the structure upright. Having only two base parameters of elasticity one for the strings and one for the bars make the model more efficient computationally. The model was made into three forms representing squamish tissue – short model, cuboidal tissue – medium sized model, and columnar tissue – tall model. These models were then tested using physiological ranges of size, force, attachments, and prestrains in both tension and compression. The resulting force-distance and stress-strain curves were evaluated and found to have both linear and non-linear slopes. The stress-strain curves were shown to model real tissue in tension and compression. The models developed were compared to data from tissue and found to closely match the data for the tissue. The factors that influence the mechanics of the tissue model are the cytoskeleton, the cell attachments, and the base attachments, and these are the known factors that influence the mechanics of cell sheets. The models are adjustable by modifying the values of the strings and bars of the tensegrity models and the test conditions.