Dedicated to Prof. Demeter Krupka in his 65th birthday.-- 11 pages.-- MSC classes: 70G50, 58F05.In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections.This work has been partially supported by MEC (Spain) Grants MTM 2006-03322, MTM 2007-62478, project "Ingenio Mathematica" (i-MATH) No. CSD 2006-00032 (Consolider-Ingenio 2010) and S-0505/ESP/0158 of the CAM.Peer reviewed