The issue of the tree falling in the process of its felling by flexible saw chains (FSC) in the multidimensional space is considered in the article. It is proved that the falling tree makes the fall not in the plane, but performs a more difficult movement with some rotation and deviation of the actual falling plane from the geometrical. The process of the tree fall in sawing by FSC is reduced to the problem of the absolutely rigid body motion having the fixed point in Lagrange-Poisson variant. Six equations are made in this case, at the solution of which the tree fall time and the deviation angle of the actual falling plane from the geometric are determined.