It is known that a spot weld is a much more rigid connexion between two sheets than a rivet, and that this is likely to have some bearing on the relative strengths of the two types of joint. A recent test has emphasized this point. A spot-welded box, identical with a riveted box except that spot welds replaced rivets, failed at about two-thirds of tie failing load of the riveted box in spite of the fact that the shear strength of an individual spot weld was nearly twice that of a rivet, as determined by tests. In this paper the problem is examined theoretically on the basis of experimentally obtained stress-strain curves for riveted and spot-welded joints in shear. The theoretical treatment takes account of the plastic, as well as the elastic, part of the stress-strain curves, and examples are given of the relative behaviour of the two types of joint in certain simple structural elements. A multi-row lap joint is the first example chosen, and the second is a stringer reinforced panel in which there is appreciable shear-lag. In each example the riveted specimen gives the higher failing load (assuming the fastenings fail and not the connected members), although the experimental failing load of the individual rivet is less than half that of the spot weld. For lower loads, curves are shown which indicate the radical change that takes place in the distribution of shear among the rivets and welds, as more and more of them are loaded beyond their yield points. While such changes are of only incidental interest so far as the ultimate failing load of the structure is concerned, they are of paramount interest when assessing the life of the structure under repeated loading at loads that may be small compared with the ultimate load, for the distribution of shear among the fastenings is then clearly an important consideration. The shear-lag case is of interest as showing how the difference between rivet and weld shear flexibility tends to be masked by that of the sheet panel connecting the booms and stringers. It is therefore a useful example for emphasizing that the character of the structure must be taken into account, as well as the individual properties of the fastenings, when comparing the likely behaviour of rivets and welds.