Summary: ``In this paper a set of elliptic curves $E$ with explicit elements of order 3 in their Tate-Shafarevich group is constructed. First, the theory of descent by 3-isogeny is reviewed, including explicit equations for homogeneous spaces representing the elements in the associated Selmer group. For the main result, elliptic curves admitting a rational 2-isogeny as well as a rational 3-isogeny are constructed. Using elementary 2-isogeny descent, it is shown that our curves have rank zero. A result of Cassels then shows that the Selmer group of the 3-isogeny is non-trivial. As a consequence one obtains in a very simple way explicit examples of plane cubics over $\Bbb Q$ that have a point everywhere locally, but not globally.''