Special balloons with hermetic cabins were constructed and launched during the 1930s to explore high altitudes beyond the reach of airplanes. In the USSR, the semi-amateur society Osoaviakhim attempted the development of such aerostats; the military, at least initially, supported its efforts as useful for its pursuit of high-altitude aircraft. The first Soviet stratospheric balloon "SSSR-1" reached the altitude of 19 km in September 1933, breaking the previous record set by the Belgian scientist A. Piccard. The following year "Osoaviakhim-1" reached 22 km, but an accident during descent destroyed the cabin and killed the crew. "SSSR-lbis" of 1935 provided the greatest success as measured by scientific results, although a hydrogen leak nearly brought about another tragic end. Two navigators parachuted out, while the third managed to land with the cabin. Archival investigations have uncovered several other failed launches of gigantic stratostats - "SSSR-2", "SSSR-3", and "Osoaviakhim-2" in 1934-1940 - and provided the means to analyze the causes of accidents. The prevailing regime of secrecy did not allow free publication about these apparata. The military eventually decided to put a halt to uncoordinated, semi-amateur attempts and transfer the program of stratospheric flights under the supervision of the Academy of Sciences. The war interrupted the activities and brought the stratostat program to an end.