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Earlier work has shown that by bonding tensioned flexible recording media to rigid support disks it is possible to have performance features similar to rigid disks, while retaining the advantages of flexible-media technology. The present paper documents the use of a mathematical model of the head, suspension, air bearing, and tensioned medium to design nearly optimal sliders for a given applied tension and medium stiffness. A novel coupled finite difference algorithm for solving the governing partial differential equations is described which allows the medium to be modeled in polar coordinates and the head and air bearing to be modeled in rectangular coordinates. Realistic medium boundary conditions are imposed allowing the head position to vary from the inside radius to the outside radius of the disk. Slotted spherical sliders are modeled and model predictions are compared to white-light interferometric measurements of the head-to-medium spacing. Measured friction and modeled minimum head-to-medium spacing are plotted versus velocity. Modeled minimum spacing becomes greater than the disk surface roughness near the velocity of minimum friction.