This research presents the initial studies and results on shield design for Shape-Shifting Surfaces (SSSs) seeking maximum compression and maximum expansion of a unit-cell. Shape-Shifting Surfaces (SSSs) are multilayered surfaces that are able to change shape while maintaining their integrity as physical barriers. SSSs are composed of polygonal unit-cells, which can change side lengths and corner angles. These changes are made possible by each side and corner consisting of at least two different shields, or layers of material. As the layers undergo relative motion, the unit-cell changes shape. In order for the SSS to retain its effectiveness as a barrier, no gaps can open between different layers. Also, the layers cannot protrude past the boundaries of the unit-cell. Based on these requirements, using equilateral triangle unit-cells and triangular shields, a design space exploration was performed to determine the maximum deformation range of a unit-cell. It was found that the triangular shield that offered maximum expansion and compression ratio is a right triangle with one angle of 37.5 degrees and its adjacent side equal to 61% of the side of the unit-cell. The key contribution of this paper is a first algorithm for systematic SSS shield design. Possible applications for SSSs include protection, by creating body-armor systems; reconfigurable antennas able to broadcast through different frequencies; recreational uses, and biomedical applications.