A Finsler manifold is a Riemannian manifold without the
quadratic restriction. In this paper we introduce the energy
functional, the Euler-Lagrange operator, and the stress-energy
tensor for a smooth map $\phi$ from a Finsler manifold to a
Riemannian manifold. We show that $\phi$ is an extremal of the
energy functional if and only if $\phi$ satisfies the
corresponding Euler-Lagrange equation. We also characterize
weak Landsberg manifolds in terms of harmonicity and
horizontal conservativity. Using the representation of a
tension field in terms of geodesic coefficients, we construct
new examples of harmonic maps from Berwald manifolds which are
neither Riemannian nor Minkowskian.