Summary: A family of composite black brane solutions in the model with scalar fields and fields of forms is presented. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat “internal” spaces. The solutions are governed by moduli functions \(H_s\) (\(s = 1, \ldots, m\)) obeying non-linear differential equations with certain boundary conditions imposed. These master equations are equivalent to Toda-like equations and depend upon the non-degenerate (\(m \times m\)) matrix \(A\). It was conjectured earlier that the functions \(H_s\) should be polynomials if \(A\) is a Cartan matrix for some semisimple finite-dimensional Lie algebra (of rank \(m\)). It is shown that the solutions to master equations may be found by using so-called fluxbrane polynomials which can be calculated (in principle) for any semisimple finite-dimensional Lie algebra. Examples of dilatonic charged black hole (\(0\)-brane) solutions related to Lie algebras \(A_1\), \(A_2\), \(C_2\) and \(G_2\) are considered.