You can still buy civilian Uzi lookalikes, which IIRC were made by a few companies prior to the '94 ban (Vector Arms was one, I think). Unlike the real Uzi, which originally fired from an open bolt, the civilian lookalikes fire from a closed bolt. In other words, in the original Uzi, the bolt is held back by the firing mechanism until you pull the trigger, which lets the bolt fly forward, strip a round from the magazine, chamber the round, and fire it. Civilian lookalikes don't hold the bolt back; when you pull the bolt back and let it go, the bolt flies forward to chamber a round but does not fire it; pulling the trigger then releases an internal hammer or striker to fire the gun. They had to do that because guns that fire from an open bolt are relatively easy to convert to full-auto, so the National Firearms Act treats them as restricted Title 2 machine guns (even if not actually converted).
Civilian Uzi lookalikes were available in two basic configurations, a short-barrelled model that was legally considered a pistol and had no stock (pistols with stocks are controlled by the NFA), and a 16" barrel model that was legally considered a rifle and could have a shoulder stock. I have seen models with an authentic-looking collapsible or folding stock like a real Uzi, and I've seen models with fixed wooden stocks.
The only way to get a realistic-looking Uzi lookalike (with stock AND short barrel) would be to buy the carbine version, go through the extensive paperwork to register it as a "short-barreled rifle" under the NFA, and then have the barrel shortened to the correct length.
Civilian subgun lookalikes are nowhere near as popular as AR-15's and civilian AK lookalikes, possibly because an Uzi lookalike is incredibly heavy and bulky for a 9mm. My wife's Glock 26 fires the same ammunition at the same rate of fire as a civilian Uzi lookalike, and measures less than 13cm x 8.5cm. IMHO, bulky pistol-caliber carbines just aren't very size-efficient. (They are cool-looking, though.)