The evolutionary origin of the long neck of giraffes is enigmatic. One theory (the ‘sexual selection’ theory) is that their shape evolved because males use their necks and heads to achieve sexual dominance. Support for this theory would be that males invest more in neck and head growth than do females. We have investigated this hypothesis in 17 male and 21 female giraffes with body masses ranging from juvenile to mature animals, by measuring head mass, neck mass, neck and leg length and the neck length to leg length ratio. We found no significant differences in any of these dimensions between males and females of the same mass, although mature males, whose body mass is significantly (50%) greater than that of mature females, do have significantly heavier (but not longer) necks and heavier heads than mature females. We conclude that morphological differences between males and females are minimal, that differences that do exist can be accounted for by the larger final mass of males and that sexual selection is not the origin of a long neck in giraffes.