Cross takes tighthead prop Murray's place in the team that will face Ireland at Murrayfield this weekend, as the committed Christian continues to make himself unavailable for selection on Sundays. Only Ireland's Cian Healy and Mike McCarthy have made more tackles than the 25 managed by the Worcester man in the Scots' opening two games against England and Italy.
But interim head coach Scott Johnson has already informed Cross that a positive performance against the Irish could result in Murray surrendering his place for longer than just one game, and Cross said: "Do I feel unlucky to have someone like Euan in front of me? No. I enjoy the contest. The competition can be frustrating when you come second in the selection contest. But it's a driver to improve, and that sort of pressure forces you to improve.
The Edinburgh player, though, does not feel threatened by his team-mate's possible return, and claims they are both working for a common cause.
The 30-year-old told Press Association Sport: You don't want to be in a comfort zone when you are looking to perform at an elite level, which we are.
"Is Euan a rival? Yeah, but it's a constructive rivalry - through the competition that tighthead props have in squad, we'll challenge each other to be better.
"It won't always be comfortable, it won't always be nice, but we are all in to do the same thing, which is to be better and get picked."
Cross also acknowledged that he could be back on the bench himself if he does not match those first two displays by Scotland's top defensive performer.
He said: "It's important personally to get a chance to show your coaches why they should pick me.
"There's also a risk that I provide them reasons to see why not to pick me. It's important that I give them plenty of the former, none of the later."
England's victory in the opening-day Calcutta Cup clash and their triumph over Ireland a fortnight ago has put them on course for the Grand Slam, leaving Scotland, Italy, Ireland and Wales all on one win each, with France yet to register a success in this year's competition.
But the tight nature of the tournament could yet play into Scottish hands, according to Cross.
He said: "I think with only one side still on for the Grand Slam, it's still a very open championship - principally because of the upset in the first week when Italy beat France.
"That's very exciting for us. An open championship is a good opportunity for all teams. We are one of those teams and we want to be in the mix when it comes down to the wire. And the way we are going to do that is to beat Ireland on Sunday."