The two exciting Academy products have both impressed in recent league games and have now been given starting spots by Head Coach Danny Wilson.
There are six changes in total to the team that started the recent clash with Leinster on home soil.
Wales wing Tom James is released from international duty and lines up in a new-look back line.
The starting line-up also features a call-up for Aled Summerhill at outside centre while Dan Fish returns at full back.
Loosehead prop Thyer gets his chance to shine alongside recalled hooker Matthew Rees in the front row. Josh Turnbull is again released by Wales to play in the back row.
The bench includes Kristian Dacey, the final player to be released from the Welsh international set-up for the fixture, and recalls for Lewis Jones, Jarrod Evans and Garyn Smith.
Head Coach Danny Wilson said: “It’s another crucial home game at a venue where we are always extremely motivated to win.
“We are back in front of our passionate home supporters and we were very disappointed to lose last weekend. We need to bounce back with a win.
“Ulster are a good side, home or away they always perform, and they have depth to their squad, despite international call-ups.
“They are a very dangerous side and they will be motivated by the narrow loss to Scarlets last weekend. Ulster play good open rugby so it should make for an entertaining game.
"Tomos Williams and Brad Thyer have both impressed in recent games and deserve starting positions. We're looking forward to seeing how they both perform from the start of the game."
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Cardiff Blues: 15 Dan Fish, 14 Blaine Scully, 13 Aled Summerhill, 12 Rey Lee-Lo, 11 Tom James, 10 Rhys Patchell, 9Tomos Williams; 1 Brad Thyer, 2 Matthew Rees, 3 Salesi Ma’afu, 4 Jarrad Hoeata, 5 James Down, 6 Josh Turnbull, 7 Ellis Jenkins, 8 Manoa Vosawai
Replacements: 16 Kristian Dacey, 17 Thomas Davies, 18 Taufa’ao Filise, 19 Macauley Cook, 20 Josh Navidi, 21 Lewis Jones, 22 Jarrod Evans, 23 Garyn Smith