The floating-body forms having two frequencies at which no heaving force is exerted in waves are considered in this paper. It is found by applying Chou's method that the floating-body forms possess the constricted part between the free surface and the bulbous part in the water. Heaving forces of several cylinders with the cross sections of the wave-free forms are calculated by source method and measured in wave-excitation experiments. Both results of the calculation and the experiment confirm that heaving forces vanish at two frequencies. Secondly, investigations are made for a catamaran composed of such cylinders and a vertical body of revolution whose profile is similar to the cross section of one of the cylinders. It is also the case for these bodies to have two wave-free frequencies.