The three strategically important bridges are located in Russian-controlled areas and have been attacked within a few days. Without them, Russia will have difficulty sending reinforcements to the invaded border areas. The Russian forces also risk being trapped between the river, Ukrainian resistance, and Ukraine's border.
They may be forced to withdraw, according to Ukrainian military analyst Mykola Bjeljeskov.
Attacks on the bridges complicate or even prevent the enemy from maintaining their forces south of the Sejm River, he says to The New York Times.
If the Ukrainian forces advance to the riverbank, they create a natural barrier against potential Russian attacks, the newspaper writes.
Over two weeks
A Russian military investigator confirmed on Monday in a Russian propaganda channel that Ukraine had "completely destroyed" one bridge and damaged two others. A number of Russia's influential and regime-loyal so-called military bloggers report the same thing.
Roman Alechin, an advisor to the governor of Kursk, announces that Russian forces have begun building pontoon bridges to facilitate logistics. Several such bridges can be seen in satellite images.
The Ukrainian surprise counteroffensive into Russia has been going on for over two weeks. It has exposed weaknesses in the Russian defense when Ukrainian forces quickly managed to penetrate Russian territory.
One purpose of the counter-invasion appears to be to divert Russian forces from the heavily pressured front line in eastern Ukraine. So far, this has only happened to a limited extent, and the invasion forces are continuing to advance towards the city of Pokrovsk in Donetsk.
Major drone attack
Ukraine continues to attack other parts of Russia. During the night to Wednesday, eleven Ukrainian drones were shot down in the air around Moscow, according to the mayor of the Russian capital.
"This is one of the largest attempts to attack Moscow with drones so far", writes Mayor Sergey Sobyanin on Telegram.
No damage or fatalities have been reported after the attack, according to him.
Drone attacks on Moscow are rare. The last time was in May when Russia reported that they had shot down a drone there, which led to traffic being stopped at two major airports for over an hour.
According to Russian authorities, a total of 45 Ukrainian drones were shot down over various parts of Russia during the night. Many were directed towards another border region, Bryansk.