Nuclear anapole moments of ¹³³Cs, ^203,205Tl, ²⁰⁷Pb, ²⁰⁹Bi are treated in the single-particle approximation. Analytical results are obtained for the oscillator potential without spin-orbit interaction. Then the anapole moments are calculated numerically in a Woods-Saxon potential which includes spin-orbit interaction. The results obtained demonstrate a remarkable stability of nuclear anapole moment calculations in the single-particle approximation.