Rhiwbina make the short trip to Senghenydd knowing that they already have a Two East league victory over their hosts.
"We are delighted to have reached this stage of the competition for the first time," said Squirrels press officer John Humphreys.
"We won 22-10 at Welfare Park earlier in the season and are presently on an eleven match unbeaten run, so we are quietly confident of making it to the last 16."
Merthyr's trip to Ystrad Rhondda will be the most closely-contested tie of the round. The Ironmen are joint leaders in One East while Ystrad Rhondda are close behind in third spot.
"Losing out at the semi-final stage in the last two seasons has been tough," said Ystrad secretary Alan Sinclair. "Hopefully it can be our season this year."
Ystrad beat Merthyr 28-18 in the league at The Wern in October, so with home advantage they may just have the edge.
Newcastle Emlyn face the long trip to Nant Conwy with the Red and Whites hoping the journey will be worthwhile, but there is sure to be a One North side in the last 16 as Caernarfon welcome Denbigh to Y Morfa having already recorded a 22-7 success over their visitors.
One West sides Cwmllynfell and Waunarlwydd meet at Parc y Bryn where last weekend's league match was postponed due to the weather. Waunarlwydd won the opening day fixture between the sides at their Roseland Road ground and may just be slight favourites to stay in the competition at their host's expense.
In an all-One East tie, Nelson welcome a Rumney side having already defeated them 23-16 at The Park earlier in the season. The Cardiff-based outfit are going well in the league and the Unicorns will have their work cut out to match that victory.
Whitland scraped through the last round after a 9-6 victory at Tenby and the Borderers have been rewarded with a home tie against fellow One West side Kidwelly. A 13-5 home win in the league over the Black and Ambers in November should give Whitland the confidence to make further progress.
Llantrisant were beaten quarter-finalists last season and the Two East side travel to Maesteg Quins of Two West where they can expect a tough encounter.