Uniformly loaded shallow shells whose shape conforms to an elastic membrane inflated by internal (air) pressure are often referred to as membrane shells. They are advantageous since no bending moments but only axial (membrane) stresses occur. In the present paper, membrane shells are defined analytically on circular, elliptical, and various regular-polygonal boundaries. The analytical results are verified by membrane tests, whereas the deflections of the inflated membranes are mapped by using a reflection-type Moire method. Design applications are introduced and cases of some irregular boundaries are also dealt with.