Transonic shocks play a pivotal role in designation of supersonic inlets and ram-jets. For the three-dimensional steady non-isentropic compressible Euler system with fric-tions,we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections. In this article,we are devoted to proving rigorously that a large class of these transonic shock solutions are stable,under multidimensional small perturbations of the up-coming supersonic flows and back pressures at the exits of ducts in suitable function spaces. This manifests that frictions have a stabilization effect on transonic shocks in ducts,in con-sideration of previous works which shown that transonic shocks in purely steady Euler flows are not stable in such ducts. Except its implications to applications,because frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system,we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.