The cathedral is among the city’s landmarks that were damaged in 5.8-magnitude quake that shook the Washington area in August.
Both landmarks have been undergoing stabilization and inspections since August.
Most recently, the team of rappellers that inspected the Washington Monument for cracks and loose pieces began an inspection of the cathedral’s towers.
The cathedral’s inspection began Monday and engineers are expected to work on the west towers this week.
Initial repairs are estimated to cost $15 million. Church officials plan to reopen the cathedral Nov. 12.