Someone asked me about this at the club meeting and apologies for not replying sooner...!
The Soviets apparently did consider using piston-powered cruise missiles in World War II, but details are vague and in any case nothing came of the efforts. More significantly, in October 1944, the British sent the remains of a V-1 that had been shot down over England to the USSR. The Soviets found it very interesting and promptly set up a design bureau, designated "OKB-51" to reverse-engineer it. The team was led by Vladimir Chelomei, who would later become famous for directing development of the big Soviet Proton space launch booster.
The V-1 provided by the British was lacking a few significant parts, but special Red Army detachments assigned to collect "loot" in the wake of the advance of front-line troops were able to provide more gear. The Mittelwerk facility at Nordhausen fell into the Soviet zone of control of occupied Germany, and though the Americans had hastily cleaned a great deal of gear out of the mine before the Red Army arrived, there was still material left over.
In any case, by early 1945 the Chelomei group was building copies of the V-1, designated the "10Kh" (roughly meaning "X-10" since the Cyrillic "Kh" character resembles an "X"). By April, test flights were being performed over the steppes of Central Asia with the missiles launched from Petlyakov Pe-8 heavy bombers. Work was also performed on a ship-launched variant, the "10KhN", and a ground-launched variant, the "10KhM", but flight tests showed the missiles to be unsatisfactory both in capability and reliability, and so OKB-51 went back to the drawing board, building a "14Kh" with twin pulsejet engines, a triple-fin tail, and many improvements. It was followed in turn by the "16Kh", with a similar configuration but a twin-fin tail.
The only kit I am aware of is the AMC Models Russian Missile 16Kh, 1/72 scale, kit no. 7202
The kit comes as 25 pieces cast in a light yellow/tan resin. The parts are generally well done with only a few pinholes on the nose and wings. The fuselage is solid and comes in two pieces, a nose section and a tail section, split vertically directly in front of the wings. There are no decals. For the price of this kit I would have expected some photo-etched pieces for the engine screens and possibly for the pitot-heads but none are included. Panel lines are engraved. Most are well done being nice and straight but some, in particular the access panels are not so straight (almost as if they were done free hand on the master). On my sample copy, the left wing was slightly warped. The vertical stabilizers lacked rudder lines on the rear sides, which will have to be scribed. The lines representing the elevators are straight on one side but crooked on the other. I'll be tempted to built the kit straight out of the box. The kit has four subassemblies: airframe, the engines and transport cart.
There are no locating marks for anything except the wings, which will make it difficult to determine exactly where to place the rear horizontal stabilizers and the engine pylons. There is no detailing for the engine inlets. It would have been nice to have some photo-etched parts here too. The tubes for the exhaust are solid with a small indent at the outlet. I would have preferred it if the kit had used plastic tubes instead. I will replaced them myself using those from the Frog or Airfix V1.
All in all, this definitely one of the better resin kits I have seen, but doubt it'll be “a walk in the park” build. The kit is expensive and I'd only recommend getting this one if you really need to have it in your collection.