Deformability of hydrostatic bearings could potentially increase their application range significantly. When a bearing is made compliant, the film pressure starts to influence the deformation of the support itself. This effect, called compliant-hydrostatic pre-loading, is especially crucial to take into account when designing highly deformable hydrostatic bearings. This work introduces the principle of pressure profile matching to minimize the effect of this pre-loading. A two-dimensional design model is introduced to determine the performance of such an elastic bearing utilizing stiffness profile matching. Additionally, an extension to the model is presented to analyze the basic performance of these type of bearings over small counter surface eccentricities. Finally, an embodiment of such a material distribution is presented utilizing functionally graded materials. These embodiments are analyzed with respect to their failure behavior, showing an improved shear stress and strain energy density distribution with the functionally graded supports when compared with conventional elastic supports.