given an algebraic variety x over a field f (e.g. number fields, function fields), a natural question is whether the set of rational points x(f) is non-empty. and if it is non-empty, how many rational points are there? in particular, are they zariski dense? do they satisfy weak approximation? for cubic hypersurfaces defined over the function field of a complex curve, we know the existence of rational points by tsen' s theorem or the graber-harris-starr theorem. in this talk, i will discuss the weak approximation property of such hypersurfaces.