Nicola Payne went missing from the Wood End area in December 1991. She was 18 and had a six-month-old son.
West Midlands Police began searching parkland off Purcell Road on Tuesday after receiving new information.
Nicola Payne Nicola Payne was last seen near to the Black Pad in Wood End on 14 December 1991
Det Ch Insp Matt Markham said a 74-year-old man and a 45-year-old had been arrested on suspicion of conspiring to prevent the lawful burial of a body.
He said the arrests of the men, both local to Coventry, were "directly linked" to the new information police officers had been given.
"News of these arrests may cause people to reconsider their position and if they haven't so far felt able to come forward with information, then I would urge them to now do so in light of these arrests," he said.
Excavation work
DCI Matt Markham, from West Midlands Police, said the pair were being questioned in Coventry
The latest search has focused on a section of woodland and involved using specially-trained dogs along with ground X-ray and metal detection equipment.
Police said reasonable progress was being made with clearing the ground with a view to some excavation work taking place later in the search.
Det Ch Insp Markham said: "We're committed to doing a detailed and thorough job, we owe that to Nicola's family and friends and the community of north east Coventry for whom this was a significant event."
Police are also searching an address in nearby Miles Meadow in connection with the investigation.
Miss Payne's parents, John and Marilyn, said they were being kept fully informed by officers.
In a statement, released through the police, they said: "As there is a lot of information for us to currently take in, we would please ask that you respect our privacy while this is happening.
"We hope the arrests and activity will allow anyone who may have important information to come forward and speak to the police.
"We can then finally find out what has happened to Nicola."
Miss Payne was last seen near to the Black Pad in Wood End on 14 December 1991.
In 2007, a man was arrested in connection with her disappearance and released on bail.
No-one has been charged in connection with the case.
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