Beginning in 1936, two brothers František (1914–1954) and Mojmír (1924–2011) Stránský, the owners of a bicycle repair shop in the market town of Parník (today part of C Trebova, began the design of a small, cheap three-wheeled car, inspired by three-wheelers from Morgan Motor Company. In 1943, they built their first prototype using steel tubing wrapped by dural sheet metal and some bicycle parts (later these would be replaced by parts from motorcycles). They named the vehicle Oskar ("kára na ose," or "car on axle").
In 1945, the brothers built their first batch of cars, using leather cloth instead of sheet metal as the bodywork. Three vehicles were powered by 150 cc (9 cu in) CZ motorcycle engines, three with 6 bhp (4 kW; 6 PS), 300 cc (18 cu in) PAL engines and six with 250 cc (15 cu in) Jawa units. The price was about a quarter of the cost of a typical car. The post-war Czechoslovakian auto industry was unable to meet popular demand for vehicles, resulting in long waiting periods and quotas. Several models of small cars had been built either by amateurs or in small runs (e.g., Kreibich, TRIGA Tripolino, JAB).
In 1950, the Stránský's workshop was transferred to Velo, a small manufacturing company in Hradec Kralove, later renamed to Velorex. In 1951, the machinery and six workers were moved into a new plant in Solnice. During that year, 120 Oskar 54 vehicles were produced; a year later, 180; and in 1954, eighty workers produced 40 vehicles per month. On January 21, 1954, František Stránský died when a test prototype crashed. His brother, Mojmír, refused membership in the Communist Party od Czechoslowalia and was fired. In 1956, the vehicle's name was changed to Velorex - Oskar and then just to Velorex. In 1959 the company produced 120 vehicles per month. In 1961 part of the production moved into a new plant in Rychnov nas Kneznou. The maximum speed of the car was 30 km/h. In 1963, production of the newly designed "Model 16" started (fitted with either ČZ 175 or Jawa 350 type 572 engines); and the model was modernized again in 1968. In 1971, production of three-wheeled cars stopped, and the company switched to production of a four-wheeler, the "Model 435-0", which featured the Jawa 350 type 572 - 04 engine. Problems in design and manufacturing, as well as the inability to compete with higher-category cars (including the cheap Trabants), made the four-wheeler a commercial failure, and its production was stopped in 1973. Plans to produce a small car similar to Fiat 500 did not materialize.