Step 1: Recall the definition of a principal plane.
In stress analysis, at any stressed point there exist certain special planes on which the resultant stress acts purely perpendicular to the plane surface, with no sliding component along the plane.
Step 2: Connect this to what shear stress represents.
Shear stress is precisely the component of stress that acts along, or tangential to, a plane, so if a plane by definition has no tangential component at all, its shear stress value has to be nil.
Step 3: Contrast with where shear stress is largest.
It is worth remembering that shear stress actually reaches its maximum value on planes inclined at 45 degrees to the principal planes, which makes the zero value on the principal plane itself stand out even more clearly by comparison.
Step 4: State the final answer.
So by the very definition of a principal plane, the shear stress acting along it is zero.
\[ \boxed{\text{Zero}} \]