Town face a difficult challenge against Championship side Brentford, who include former Shrews star Ryan Woods, in a Montgomery Waters Meadow clash on July 21.
They have also announced warm-up fixtures at AFC Telford (July 25) and Port Vale (July 28). Those three will be preceded by further games to be announced in due course. The League One season begins on August 4.
“Brentford are a strong opposition and it will be another good game for us, where it will be a bit more of a test of our fitness than probably the other two,” Askey said.
“The Telford game is just about getting our legs going and getting 90 minutes under our belts.
“The Port Vale game is a little bit of a stronger game, more like what we will expect on a Saturday, so they are two good games for us and local as well, which is important because it makes it easy for the supporters to go and watch the games.”
Town beat four Championship sides during last summer’s pre-season on their way to a thrilling League One campaign.
Askey added: “The main thing is fitness, getting the team to play together, me having a look at them and finding out which is the best way to play, but the main thing is getting through pre-season without any injuries. Whatever game we go into it’s about us stamping our authority on games.”