As the United States and Soviet Union warily eye one another during the Cold War, the destroyer USS Bedford is on patrol in the North Atlantic Ocean. A Navy helicopter ferries two men out to the ship in mid-ocean. One is civilian photo-journalist Ben Munceford (Sidney Poitier); the other is new ship's medical officer Commander Chester Potter (Martin Balsam). It is immediately obvious how tightly the ship is run by its skipper, Captain Eric Finlander (Richard Widmark).
The hard-boiled captain seems to take an immediate dislike to both new arrivals. Commander Potter is a Reserve Naval Officer, making him suspect with Finlander. Munceford's pointed questions and persistent meddling also rankle the captain. Finlander runs his ship under wartime conditions, keeping his men on a razor's edge.
Potter and Munceford are soon introduced to Commodore Wolfgang Schrepke (Eric Portman), a former Kriegsmarine U-boat officer serving as a NATO technical adviser aboard the Bedford. The Bedford is operating in the Denmark Strait, between Greenland and Iceland. Finlander is tracking a specific Russian submarine nicknamed "Big Red" and watching several possible "mother ships" in the area, in hopes of coming upon the rendezvous between submarine and supply ship. The Russian supply ship is soon identified as the Novo Sibursk.
Finlander's iron discipline seems to fall most heavily on young Ensign Ralston (James MacArthur), a former star quarterback whose earnestness and desire to please annoys Finlander. The Executive Officer, Commander Buck Allison (Michael Kane), warns Finlander that he is being too hard on Ralston. He is becoming jumpy and prone to mistakes.
While skirting the edge of the ice shelf, the Bedford's lookouts spot the periscope and snorkel of a Russian sub. Bedford's bookish sonar operator, Queffle (Wally Cox) reports that the Russian sub is two miles inside Greenland's territorial waters. Finlander immediately seeks a confrontation, asking NATO for permission to force the sub to the surface. NATO refuses Finlander's request. Incensed, he maintains battle stations. Even though Big Red steers back into international waters, Finlander keeps the pressure on the submarine. The submarine crew is slowly running out of air, and Finlander wants to be there when she surfaces.
Munceford eventually secures a private interview with Finlander. He tries to badger Finlander into saying something rash about attacking the enemy, but Finlander doesn't take the bait. Finlander's pursuit of Big Red now becomes a dangerous obsession. Finlander belatedly gets permission to force the sub up, providing it is still in territorial waters, but the Russian vessel has eluded him in a field of icebergs. Despite Schrepke's stern advice to stand down and de-escalate, Finlander keeps pressing. He is rewarded when the desperate Russian submarine commander briefly comes to periscope depth. Schrepke warns Finlander that the sub is now in international waters and the crew in desperate need of air. He is dealing with a desperate quarry, and the results could be unpredictable and tragic. Schrepke bluntly tells Finlander that he finds him frightening.
When the Russian sub fails to respond to Finlander's order to surface immediately, Finlander steers for the submarine's periscope and air snorkel, intending to pass directly over it. Contact is made, however. Both Schrepke and Munceford plead with Finlander to back off, telling him that he is forcing the Russians to fight. Finlander is undeterred, ordering a nervous Ensign Ralston to arm the ASROC rocket-propelled torpedo system. As the pressure-charged situation intensifies, Schrepke begs Finlander once again for restraint. The reckless captain replies, "Don't worry, Commodore. The Bedford will never fire first. But if he fires one, I'll fire one." Hopelessly rattled from Finlander's constant barking, Weapons System Officer Ralston complies with the order he thought he just heard. "Fire One!" Ralston triggers the firing switch. The ASROC roars from its tube as Finlander and Allison leap across the bridge in hopes of disarming it. They are too late. The torpedo arcs high into the sky before plunging into the sea. Seconds later, a tremendous explosion confirms the submarine's destruction. All eyes turn accusingly to Finlander. There is only stunned silence on the Bedford's bridge. Suddenly, the sonar operator frantically reports a spread of four torpedoes bearing down on the Bedford. The Russian sub had fired her torpedoes defensively as soon as the ASROC broke the surface. Finlander orders emergency evasive maneuvers and countermeasures, but it is too late. The nuclear-armed torpedoes streak remorselessly toward Bedford, which is soon enveloped in a mushroom cloud.