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We consider regular surfaces $M$ that are given as the zeros of a polynomialfunction $p:R^3\rightarrow R$, where the gradient of $p$ vanishes nowhere. Weassume that $M$ has non-zero mean curvature and prove that there exist only twoexamples of such surfaces, namely the sphere and the circular cylinder.

On regular algebraic surfaces of $R^3$ with constant mean curvature