The study of the space \({\mathcal M}{\mathcal F}\) of measured foliations on a closed surface originates in Thurston’s work on diffeomorphisms of surfaces and their action on Teichmüller spaces. Thurston has shown that \({\mathcal M}{\mathcal F}\) can be organized as a PL manifold and it carries in some sense a natural symplectic structure. In the present paper the author investigates the piecewise-linear symplectic geometry of \({\mathcal M}{\mathcal F}\). Namely, he associates to an arbitrary element \({\mathcal G}\in {\mathcal M}{\mathcal F}^ a \)flow \((F_ t^{{\mathcal G}})_{t\in R}\) defined on the whole space \({\mathcal M}{\mathcal F}\). Then, via the duality determined by the symplectic structure between vector fields and 1-forms, one proves that \((F_ t^{{\mathcal G}})_{t\in R}\) is the Hamiltonian flow corresponding to the function \(\sum^{k}_{j=1}i({\mathcal G}_ j,.)^ 2\) on \({\mathcal M}{\mathcal F}\), where \({\mathcal G}_ 1,...,{\mathcal G}_ k\) are the components of \({\mathcal G}\) and i(\({\mathcal G}_ j,.)\), \(j=1,...,k\), are the intersection functions.