The root-mean-square (rms) surface error of a circular and equilateral triangular inflatable element subjected to pressure and isotropic tension in a faceted reflector surface is analyzed. The inflatable elements are assumed to be placed on any place of the reflector surface. Boundaries of the membrane are assumed to coincide with elliptic or hyperbolic paraboloidal surfaces. The deflection of the membrane is calculated based on the linear membrane equation (Poisson's Equation). According to the constraints of parameters which determine the boundary deflection of the membrane element, different kinds of rms error optimizations are carried out, and corresponding optimum membranes are obtained and compared. Effects of pressure/tension ratio, boundary deflection, size, etc. upon surface error of each optimum membrane are examined. The surface error of a circular and equilateral inflatable element whose boundaries coincide with the approximate parabolic surface of the reflector surface is found to be zero, on the assumption that the appropriate pressure/tension ratio is applied. The rms errors of both an optimum circular inflatable element with flat boundary and an optimum equilateral triangular inflatable element whose boundary has an equal optimum radius of curvature, are well below those of mesh elements when the elements are placed near the reflector axis. Comparison of rms error of a circular and triangular inflatable element with the same area is also carried out.