For several months, Ukraine has been using Storm Shadow—which can hit targets more than 150 miles away with pinpoint accuracy—to blow up Russian military supplies and infrastructure that until recently were out of Kyiv’s reach. The missile is so precise that in its first use, during the 2003 Gulf War, one Storm Shadow punched a hole in the side of a building and then another one followed through the same hole.
Now, Kyiv could be set to receive U.S. long-range missiles, as officials in Washington seek approval at the highest levels to send an American system to Ukraine and bolster its continuing offensive. The system, the Army Tactical Missile System, or ATACMS, has a range of about 190 miles. Washington has so far not sent it for fear that Ukraine could use the truck-launched rocket to strike Russian territory and escalate the conflict into a wider war.
Ukraine’s use of Storm Shadow over recent weeks has indicated it has lots of targets to hit within Russian-occupied parts of the country.
Storm Shadow, which entered Ukrainian service in May, has been accomplishing a mission that Ukraine last year pursued with U.S.-made High Mobility Artillery Rocket System, or Himars, a truck-based weapon with a strike range of at most 50 miles. Like Himars, which forced Russia to pull supplies and bases back from front lines to avoid being hit, Storm Shadow is compelling Moscow to rethink its logistics as Ukraine gears up its offensive.
Ukraine in June used Storm Shadows to cripple a bridge that Russia relied on to supply its troops in the Kherson and Zaporizhzhia region, Russian officials said. Days earlier, the missile destroyed a large Russian ammunition stockpile near the village of Ryokove, according to a person familiar with the matter.
Also like Himars, Storm Shadow appears to be having a psychological impact on Russian forces and civilians. Footage of the ammunition-dump hit on social media showed a string of explosions amid a raging fire and a plume of black smoke drifting across farm fields. “It’s the end,” a woman watching the destruction said on the recording.
Official Russian press and social-media channels have carried accounts of how Storm Shadow, thanks to its long reach, has struck buildings across occupied parts of Ukraine and even killed a Russian general.
Ukraine is using the weapon “very effectively,” said Doug Bush, the U.S. Army’s acquisition chief. Bush said that Ukrainian forces have been very good at linking intelligence data with high-precision, long-range strikes and “gotten inside” Russia’s ability to move its stockpiles of weapons and ammunition.
Ukrainian officials agree. In May, Ukrainian Defense Minister Oleksiy Reznikov told a local TV station that the missile has a 100% success rate in hitting its intended target. A Russian-installed official in occupied Ukraine told Russian state news agency TASS that it is hard to shoot down.
The U.K. has been a first mover in arming Ukraine. It sent antitank missiles before Russia launched its large-scale invasion last year, and London’s decision to send its Challenger 2 tanks earlier this year—the first initiative to send modern Western battle tanks to Ukraine—prompted the U.S. and other allies to follow suit.
France, which produces a twin version of the missile called Scalp, said it is considering sending longer-range missiles.
Germany continues to refrain from supplying long-range missiles because of concerns over Russian escalation and because the country needs its small inventory of such weapons for its own defense, according to two people familiar with the matter.
Britain hasn’t said how many Storm Shadows it has sent. The U.K. had roughly 822 Storm Shadows in its arsenal before the start of the war, Janes, the defense intelligence company, estimates.
The weapon’s cost may limit how many Britain’s cash-strapped Defense Ministry will be able to send. In 2011, the Royal Air Force told Britain’s Parliament that each Storm Shadow cost the equivalent of more than $1 million today.
Defense experts, though, say that its very existence in Ukraine’s arsenal, no matter how many, will have been enough to force Russia to move its supply chain further away from the front line.
“It holds a range of Russian critical dependencies at risk: fuel, ammunition dumps, command and control bunkers, and other high-value targets,” Jack Watling, senior research fellow at the Royal United Services Institute, a think tank in London, wrote in a paper on the weapon.
Storm Shadow and Scalp are produced by a British-French-Italian company, MBDA. They use a mix of guidance systems that help them evade enemy jamming, maneuver and reach their targets. Ukraine is launching the missile from Sukhoi fighter jets, the first time it has been carried by a non-Western aircraft.
Unlike better known U.S. Tomahawk cruise missiles, which are often fired in large salvos, Storm Shadow is designed to be fired in small numbers to hit very specific targets, such as the ones Ukraine has focused on. It can be set for delayed detonation, allowing it to penetrate a fortification or building and only explode once deep inside, providing a better chance of killing human targets such as soldiers or military officials.
The capability is linked to a challenge that designers set for themselves, according to a person involved in the missile’s development: Letting military planners capitalize on potential intelligence, like word that Iraqi dictator Hussein was in a bathroom deep inside one of his palaces.
“It excels at fixed targets over the horizon,” said Ian Williams, an expert on missile technology at the Center for Strategic and International Studies, a think tank.
—Bojan Pancevski contributed to this article.
Write to Alistair MacDonald at Alistair.Macdonald@wsj.com and Daniel Michaels at Dan.Michaels@wsj.com