The differential equation for the deflection of a tapered strut cannot usually be solved by formal methods; we propose to attack the problem in the reverse direction; given the deflection-curve as a polynomial, we find the shape of the longitudinal section for struts of given strength. It will appear that the shapes so found are quite different from those for struts “ of uniform stress ” yet it is possible to get substantial saving in weight for a given strength (for some of the examples up to 11 per cent., the theoretical maximum being 13.4 per cent.