  Recently proposed relations between the renormalization group functions of
the soft supersymmetry breaking terms and those of a rigid theory allow one to
consider a possibility of constructing a totally all loop finite N=1 SUSY gauge
theory, including the soft SUSY breaking terms. The requirement of finiteness,
which can be satisfied in previously constructed finite SUSY GUTs, imposes some
constraints on the SUSY breaking parameters which, in the leading order,
coincide with those originating from the supergravity and superstring-inspired
models. Explicit relations between the soft terms, which lead to a completely
finite theory in any loop order, are given.
