  The supersymmetric actions of closed multiple M2 branes with flux for the BL
and the ABJM theories have been constructed recently by Lambert and Richmond in
\cite{LR}. In this paper we extend the construction to the case of open
M2-branes with flux and derive the boundary conditions. This allows us to
derive the modified Basu-Harvey equation in the presence of flux. As an
example, we consider the Lorentzian BL model. A new feature of the fuzzy funnel
solution describing a D2-D4 intersection is obtained as a result of the flux.
