Wash and dry the cucumbers. Peel alternating strips of the green skin off the cucumber with a vegetable peeler. Slice very thinly with a mandoline-style slicer or a slicing disc of a food processor. Set aside.
Peel shallots and slice at the same thinness as the cucumber. Mix cucumber and shallots. The shallot slices will un-ravel into small rings which is what you want. Set aside.
Whisk sugar, salt and vinegar together until completely dissolved. Pour over cucumber and shallot slices, and mix well, separating the slices to make sure none of them are sticking together.
Put vegetables and all the liquid in a non-reactive (plastic or glass) container with a tight lid and refrigerate, turning occasionally for at least 3 hours or overnight before serving. Taste and adjust seasonings if necessary.