The Minstermen dominated from start to finish at Bootham Crescent, with Jon Parkin and Rhys Murphy both troubling visiting goalkeeper Brendan Moore on numerous occasions.
Parkin lobbed Moore - and the crossbar - before stabbing wide in the first half, while Murphy came closest with an attempt at the near post in the 78th minute.
Torquay's best opportunity came in the third minute, Kyle Letheren forced into a smart one-handed save to deny Ben Gerring from close range.
Report supplied by the Press Association.
Match ends, York City 0, Torquay United 0.
Second Half ends, York City 0, Torquay United 0.
Sean Newton (York City) is shown the yellow card for a bad foul.
Substitution, Torquay United. Paul Rooney replaces David Fitzpatrick.
Ben Gerring (Torquay United) is shown the yellow card.
Substitution, York City. Callum Rzonca replaces Daniel Nti.
Substitution, Torquay United. Brett Williams replaces Jamie Reid.
Second Half begins York City 0, Torquay United 0.
First Half ends, York City 0, Torquay United 0.
Rhys Murphy (York City) is shown the yellow card for a bad foul.
Jon Parkin (York City) is shown the yellow card for a bad foul.
Courtney Richards (Torquay United) is shown the yellow card for a bad foul.
First Half begins.
Lineups are announced and players are warming up.
Bottom-of-the-table York came close to securing their first National League victory since September but Torquay forced a goalless draw.