Experts on economic sanctions say the measures imposed by Washington and the European Union on Russian and Ukrainian officials will have little immediate impact.
Those travel and visa restrictions were imposed on people who pushed Crimea to join the Russian Federation.
But some analysts worry that sanctions may be strengthened soon, which could raise tensions further.
One native Russian who tracks economic issues, Misha Gutkin of VOA's Russian service, says some of the seven Russian officials sanctioned by U.S. President Barack Obama on Monday were surprised at how weak the measures were and they laughed about them.
One official, Deputy Prime Minister Dmitry Rogozin, used his Twiiter account to jokingly address the American leader as "Comrade Obama."
Some of the Russians said they have no assets in U.S. financial institutions and no intention of traveling to the U.S., negating the impact of a visa ban.
Gutkin cited the comments of Vladislav Surkov, an aide to Russian President Vladimir Putin, one of those sanctioned by the U.S.
"Vladislav Surkov said he considers [being sanctioned] an honor, and in fact he has no property or bank accounts in the United States. And the only things that he is interested in the United States are works by [poet] Allen Ginsberg, [artist] Jackson Pollock and [rap musician] Tupac Shakur, and I don't need a visa to enjoy those, he said. So far the effect is negligible," said Gutkin.
The Russian stock market advanced Monday, suggesting that investors in Moscow were not very worried by the sanctions. The United States says it may impose further sanctions if Russia continues to push to annex Crimea.
Poltical scientist Stephen Farnsworth at the University of Mary Washington says the United States is treading a fine line in imposing sanctions.
"The challenge the United States faces is how to make sanctions sufficiently painful that they will encourage more reasonable behavior from Russia, but at the same time not so painful that they are likely to trigger an escalation," said Farnsworth.
He said the West's confrontation with Russia over Crimea "is bad now, but it could easily be worse."
Bankrate.com analyst Mark Hamrick says tighter sanctions could heat up the confrontation, and that could hurt the economy.
"If things start going down a slippery slope at an accelerating rate - it’s going to be very unsettling for the financial markets, so this is definitely a key risk factor for investors to be watching," said Hamrick.
Hamrick says he hopes cool heads (reasonable people) are able to keep the situation from escalating.