The Drinfeld compactification
Bun
¯
B
′
\overline {\operatorname {Bun}}{}_B’
of the moduli stack
Bun
B
′
\operatorname {Bun}_B’
of Borel bundles on a curve
X
X
with an Iwahori structure is important in the geometric Langlands program. It is closely related to the study of representation theory. In this paper, we construct a resolution of singularities of it using a modification of Justin Campbell’s construction of the Kontsevich compactification. Furthermore, the moduli stack
Bun
B
′
{\operatorname {Bun}}_B’
admits a stratification indexed by the Weyl group. For each stratum, we construct a resolution of singularities of its closure. Then we use this resolution of singularities to prove a universally local acyclicity property, which is useful in the quantum local Langlands program.