The Paixhans gun (French: Canon Paixhans, French pronunciation: [pɛksɑ̃]) was the first naval gun designed to fire explosive shells. It was developed by the French general Henri-Joseph Paixhans in 1822–1823. The design furthered the evolution of naval artillery into the modern age. Its use presaged the end of wood as the preferred material in naval warships, and the rise of the ironclad.

Explosive shells had been used in ground warfare and against stationary targets, but not in high-velocity, flat-trajectory guns due to safety concerns. Henri-Joseph Paixhans developed a delaying mechanism that allowed explosive shells to be safely fired in high-powered guns, first demonstrated in trials in 1824. The French Navy adopted the first Paixhans guns in 1841, and the weapons eventually saw use in the 1840s by France, Britain, Russia, and the United States. The guns' effectiveness in naval combat was demonstrated in battles such as Veracruz in 1838, Campeche in 1843, and Sinop in 1853.

Although the idea was innovative, metallurgy at the time had not advanced enough for safe operation, leading to catastrophic failures in naval guns. Further developments by John A. Dahlgren and Thomas Jackson Rodman improved the weapon for both solid shot and shell use.

Explosive shells had long been in use in ground warfare (in howitzers and mortars) and on bomb vessels against stationary targets, but they were fired only at high angles and with relatively low velocities. The shells of that time were inherently dangerous to handle, and no method had been found to safely fire the explosive shells with the high power and flatter trajectory of a high-velocity gun.

However, before the advent of radar and modern optical controlled firing, high trajectories were not practical for ship-to-ship combat. Such combat essentially required flat-trajectory guns in order to have a reasonable chance of hitting the target. Therefore, ship-to-ship combat had consisted for centuries of encounters between flat-trajectory cannons using inert cannonballs, which could inflict only local damage, even on wooden hulls.

Paixhans advocated using flat-trajectory shell guns against warships in 1822 in his Nouvelle force maritime et artillerie.

Paixhans developed a delaying mechanism that, for the first time, allowed shells to be fired safely in high-powered flat-trajectory guns. The effect of explosive shells lodging into wooden hulls and then detonating was potentially devastating. Henri-Joseph Paixhans first demonstrated this in trials against the two-decker Pacificateur in 1824, in which he successfully broke up the ship. Two prototype Paixhans guns had been cast in 1823 and 1824 for this test. Paixhans reported the results in Experiences faites sur une arme nouvelle. The shells had a fuze that ignited automatically when the gun was fired; they lodged in the wooden hull of the target, and exploded a moment later:

The shells which produced those very extensive ravages upon the Pacificator hulk in the experiments made at Brest, in 1821 and 1824, upon the evidences of which the French naval shell system was founded, were loaded shells, having fuzes attached, which, ignited by the explosion of the discharge in the gun, continued to burn for a time somewhat greater than that of the estimated flight, and then exploded; thus producing the maximum effect which any shell is capable of producing on a ship.