  We consider a gravitational model on a manifold M = M_0 x M_1 x...x M_n with
oriented connected Einstein internal spaces M_1,...,M_n. The matter part of the
action contains several scalar fields and antisymmetric forms. With Ricci-flat
internal spaces, the model has a midisuperspace representation in form of a
sigma-model on M_0. The latter can be used to determine exact composite
electric p-brane solutions, which depend on a set of harmonic functions on M_0.
