  Let (M1,F1) and (M2,F2) be two Finsler manifolds. The twisted product Finsler
metric of F1 and F2 is a Finsler metric F = (F1^2+ f^2F2^2)^1/2 endowed on the
product manifold M1 * M2, where f is a positive smooth function on M1 * M2. In
this paper, Landsberg curvature and mean Landsberg curvature of the twisted
product Finsler metric are derived. Necessary and sufficient conditions for the
twisted product Finsler metric to be Landsberg metric or weakly Landsberg
metric are obtained. And it is proved that every twisted product Finsler metric
has relatively isotropic Landsberg (resp. relatively isotropic mean Landsberg)
curvature if and only if it is a Landsberg (resp. weakly Landsberg) metric.
