A non-contact seal assembly includes a plurality of seal shoes, a seal base and a plurality of spring elements. A first of the spring elements includes a first mount, a second mount and a spring beam. The spring beam extends a length longitudinally along a centerline from the first mount to the second mount. The spring beam includes opposing first and second surfaces. The first surface is disposed a first distance from the centerline, and the second surface is disposed a second distance from the centerline. The first distance and the second distance change as the spring beam extends longitudinally along the centerline to provide at least a portion of the spring beam with a tapered geometry. The portion of the spring beam has a longitudinal length that is at least about five percent of the length of the spring beam.