  We introduce the class of linearly shellable pure simplicial complexes. The
characterizing property is the existence of a labeling of their vertices such
that all linear extensions of the Bruhat order on the set of facets are
shelling orders. Coxeter complexes of weak intervals and lower Bruhat intervals
of parabolic right quotients, as type-selected Coxeter complexes of lower
Bruhat intervals of parabolic left quotients, are proved to be linearly
shellable. We also introduce the notion of linear strong shellability.
