Police and paramedics were called to Westmorland Street this afternoon (Sun April 30) after the incident at the Wakefield Car Show.
Wakefield Central Neighbourhood Policing Team tweeted: "In a freak accident, it appears that one classic car lurched forward at speed, pushing another car backwards into members of the public.
"Two people were taken to hospital, but thankfully there appears to be no serious injuries."
Around 400 cars and 150 classic motorcycles were due to be be on display at the Wakefield Car Show .
The organisers, who previously staged Silcoates Classic and American Car Show, said thousands of people were expected at today's event in Wakefield city centre.