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A straightforward method is proposed to design a class of causal, two-dimensional, infinite impulse response digital filters which possess circularly symmetric, maximally flat magnitude, low-pass responses. This class of filters has the characteristic that the numerator and the denominator of the corresponding digital transfer function individually possess approximately circularly symmetric magnitude responses. Under this condition, the proposed method requires the design of a one-dimensional transfer function satisfying the frequency selective properties and a simple modification which transforms the one-dimensional function into a circularly symmetric two-dimensional function. Low-pass filters with maximally flat magnitude are obtained and the characteristics of the resulting functions indicate that they possess good circular symmetry.